%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "1.82",
%%% date = "12 August 2015",
%%% time = "10:24:24 MDT",
%%% filename = "benfords-law.bib",
%%% address = "University of Utah
%%% Department of Mathematics, 110 LCB
%%% 155 S 1400 E RM 233
%%% Salt Lake City, UT 84112-0090
%%% USA",
%%% telephone = "+1 801 581 5254",
%%% FAX = "+1 801 581 4148",
%%% URL = "http://www.math.utah.edu/~beebe",
%%% checksum = "49030 30322 133326 1331263",
%%% email = "beebe at math.utah.edu, beebe at acm.org,
%%% beebe at computer.org (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "bibliography; BibTeX; Benford's Law;
%%% Bradford's Law; First Digit Phenomenon;
%%% Gibrat's Law; Gibrat's Rule of Proportionate
%%% Growth; Hall--Petch effect; Heaps' Law;
%%% Herdan's Law; Law of Anomalous Numbers;
%%% Lotka's Law; Pareto Distribution; Pareto Law;
%%% Pareto Principle; power law; Significant
%%% Digit Law; Simon--Yule model of text
%%% generation; Stigler's Law; Yule process;
%%% Zipf's Law",
%%% license = "public domain",
%%% supported = "yes",
%%% docstring = "This is a bibliography about a numerical
%%% curiousity variously known as Benford's Law
%%% (see particularly entries Newcomb:1881:NFU,
%%% Benford:1938:LAN, Pinkham:1961:DFS,
%%% Logan:1978:FDP, Hill:1998:FDP, and
%%% Block:2010:GEB, Nigrini:2012:BLA), the Law of
%%% Anomalous Numbers, and the Significant Digit
%%% Law: in a table of physical constants (and in
%%% many other collections of measured numbers),
%%% the leading digits do not have equal
%%% probability of occurrence: the digit 1 is
%%% more common than 2, which is more common than
%%% 3, and so on.
%%%
%%% Publications recorded here appear in about
%%% 385 different journals from accounting,
%%% aerobiology, animal behavior, auditing,
%%% astronomy, bible studies, biology,
%%% biometrics, botany, business, chaos theory,
%%% chemistry, colloid science, complexity,
%%% computer science, conflict resolution,
%%% cognitive science, criminology, critical
%%% phenomena, demographics, drug design,
%%% dynamics, earthquake detection, economics,
%%% electoral studies, engineering, entropy,
%%% expert systems, extinction, finance,
%%% forensics, gambling, geography, geophysics,
%%% human resources, hydrology, imaging science,
%%% informetrics, language science, library
%%% science, linguistics, marine systems,
%%% marketing, mathematics, medicine, networking,
%%% neuroscience, nuclear engineering, nuclear
%%% science, operations research, physics,
%%% political analysis, probability, psychology,
%%% signal processing, simulation, sociology,
%%% statistical mechanics, statistics,
%%% stock-market trading, tax accounting, urban
%%% development, and urban growth, reflecting the
%%% broad interest in the unexpected phenomenon
%%% discovered and reported first by the
%%% Canadian/American astronomer and
%%% mathematician, Simon Newcomb, in a two-page
%%% note in 1881, and then independently, and
%%% with numerical evidence from much more
%%% measured data, by American physicist Frank
%%% Benford in 1938.
%%%
%%% In Benford's Law, the frequency of leading
%%% decimal digit p is roughly log10(1 + (1 /
%%% p)): that is, approximately 0.301, 0.176,
%%% 0.125, 0.097, 0.079, 0.067, 0.058, 0.051, and
%%% 0.046 for digits 1 through 9, instead of the
%%% expected 1/9 ~= 0.111 for values taken from a
%%% uniform distribution of random numbers.
%%%
%%% Another common statement of Benford's Law is
%%% that the probability that a decimal number
%%% representing a measured value begins with a
%%% nonzero digit not greater than p is log10(1 +
%%% p), that is, approximately 0.301, 0.477,
%%% 0.602, 0.699, 0.778, 0.845, 0.903, 0.954, and
%%% 1.000 for digits 1 through 9.
%%%
%%% For the second digits, the probabilities are
%%% determined by the formula (see
%%% Todter:2009:BLI)
%%%
%%% sum(q = 1:9) log10(1 + 1 / (10*q + p)),
%%%
%%% that is, approximately 0.120, 0.114, 0.109,
%%% 0.104, 0.100, 0.097, 0.093, 0.090, 0.088, and
%%% 0.085, for second decimal digits p = 0
%%% through 9.
%%%
%%% Probabilities for later digits are even
%%% closer: see entries Newcomb:1881:NFU,
%%% Feldstein:1976:CED, and Todter:2009:BLI.
%%%
%%% Benford's Law is not restricted to decimal
%%% numbers: for base b (as long as b is not
%%% huge, according to entry Schatte:1998:BLV),
%%% just change the 10 values to b in the
%%% previous formulas. Here are some results for
%%% selected bases commonly used in computers,
%%% showing the probability of the first (D1) or
%%% second (D2) digit (first index) for base b
%%% (second index):
%%%
%%% P[D1, 2]: 1.000
%%% P[D2, 2]: 0.585, 0.415
%%%
%%% P[D1, 4]: 0.500, 0.292, 0.208
%%% P[D2, 4]: 0.304, 0.261, 0.230, 0.206
%%%
%%% P[D1, 8]: 0.333, 0.195, 0.138, 0.107,
%%% 0.088, 0.074, 0.064
%%% P[D2, 8]: 0.151, 0.141, 0.133, 0.126, 0.120,
%%% 0.115, 0.110, 0.105
%%%
%%% P[D1, 10]: 0.301, 0.176, 0.125, 0.097,
%%% 0.079, 0.067, 0.058, 0.051, 0.046
%%% P[D2, 10]: 0.120, 0.114, 0.109, 0.104, 0.100,
%%% 0.097, 0.093, 0.090, 0.088, 0.085
%%%
%%% P[D1, 16]: 0.250, 0.146, 0.104, 0.080,
%%% 0.066, 0.056, 0.048, 0.042, 0.038,
%%% 0.034, 0.031, 0.029, 0.027, 0.025,
%%% 0.023
%%% P[D2, 16]: 0.074, 0.072, 0.070, 0.068, 0.066,
%%% 0.065, 0.064, 0.062, 0.061, 0.060,
%%% 0.059, 0.058, 0.057, 0.056, 0.055,
%%% 0.054
%%%
%%% A small filter applied to the 1990 US Census
%%% data in the Project Gutenberg file
%%% uscen902.txt reports these frequencies of
%%% first and second digits for the 5148 integer
%%% values with at least 3 digits:
%%%
%%% F[D1]: 0.298, 0.215, 0.113, 0.082,
%%% 0.098, 0.056, 0.055, 0.034, 0.049
%%% F[D2]: 0.166, 0.090, 0.096, 0.081, 0.100,
%%% 0.122, 0.076, 0.073, 0.066, 0.130
%%%
%%% For the 110 numbers in the atomic weights
%%% section of the GNU units utility data file,
%%% units.dat, we have
%%%
%%% F[D1]: 0.391, 0.309, 0.045, 0.036,
%%% 0.055, 0.036, 0.036, 0.036, 0.055
%%% F[D2]: 0.173, 0.045, 0.109, 0.100, 0.145,
%%% 0.145, 0.055, 0.055, 0.091, 0.082
%%%
%%% From a snapshot of the country-area section
%%% of the US CIA World Factbook
%%%
%%% https://www.cia.gov/library/publications/the-world-factbook/rankorder/2147rank.html
%%%
%%% taken at 18 November 2011, we find 1505
%%% numbers with these frequencies:
%%%
%%% F[D1]: 0.312, 0.275, 0.100, 0.067,
%%% 0.058, 0.062, 0.046, 0.029, 0.050
%%% F[D2]: 0.167, 0.221, 0.092, 0.092, 0.062,
%%% 0.067, 0.075, 0.067, 0.083, 0.075
%%%
%%% From the country-population section
%%%
%%% https://www.cia.gov/library/publications/the-world-factbook/rankorder/2119rank.html
%%%
%%% of that book, including only the 163 values
%%% of 1,000,000 or larger, we find
%%%
%%% F[D1]: 0.301, 0.202, 0.092, 0.135,
%%% 0.055, 0.067, 0.055, 0.037, 0.055
%%% F[D2]: 0.147, 0.153, 0.110, 0.098, 0.098,
%%% 0.123, 0.086, 0.043, 0.049, 0.092
%%%
%%% From the section with the infant mortality
%%% rates per 1000 births,
%%%
%%% https://www.cia.gov/library/publications/the-world-factbook/rankorder/2091rank.html
%%%
%%% there are 208 values with at least 4 digits,
%%% with these frequencies:
%%%
%%% F[D1]: 0.361, 0.293, 0.043, 0.072,
%%% 0.062, 0.087, 0.038, 0.014, 0.029
%%% F[D2]: 0.303, 0.139, 0.077, 0.058, 0.077,
%%% 0.077, 0.106, 0.067, 0.043, 0.053
%%%
%%% In the 2010 annual financial report for IBM
%%% Corporation (its hundredth year of business)
%%%
%%% ftp://public.dhe.ibm.com/annualreport/2010/2010_ibm_annual.pdf
%%%
%%% there are 6126 numbers of two or more digits
%%% that do not look like year dates (19xx and
%%% 20xx), and they have these digit frequencies:
%%%
%%% F[D1]: 0.333, 0.160, 0.163, 0.086,
%%% 0.068, 0.053, 0.047, 0.045, 0.046
%%% F[D2]: 0.172, 0.169, 0.096, 0.084, 0.085,
%%% 0.095, 0.079, 0.074, 0.079, 0.068
%%%
%%% For the first 100,000 primes, we have
%%%
%%% F[D1]: 0.311, 0.091, 0.090, 0.087,
%%% 0.086, 0.085, 0.084, 0.083, 0.082
%%% F[D2]: 0.152, 0.151, 0.150, 0.078, 0.078,
%%% 0.078, 0.078, 0.079, 0.078, 0.078
%%%
%%% For the Fibonacci numbers, f(n), which
%%% satisfy the recurrence f(n) = f(n-1) + f(n-2)
%%% with f(1) = f(2) = 1, using the first 10000
%%% such numbers (the last of which has 2091
%%% digits), we find for the 9994 f(n) values
%%% with at least two digits these frequencies:
%%%
%%% F[D1]: 0.301, 0.176, 0.125, 0.097,
%%% 0.079, 0.067, 0.058, 0.051, 0.046
%%% F[D2]: 0.120, 0.114, 0.109, 0.105, 0.100,
%%% 0.097, 0.094, 0.090, 0.088, 0.085
%%%
%%% If we take the same set of Fibonacci numbers,
%%% we find these frequencies for values output
%%% in base 4:
%%%
%%% F[D1]: 0.500, 0.292, 0.208
%%% F[D2]: 0.303, 0.262, 0.230, 0.205
%%%
%%% The Fibonacci numbers, and the members of
%%% many other such sequences, can be proved
%%% mathematically to obey Benford's Law exactly
%%% (see entries Raimi:1976:FDP, Berger:2011:BLS,
%%% and Berger:2011:BTB).
%%%
%%% Simon Newcomb made another significant
%%% appearance in the history of science when he
%%% proposed that the then-not-understood
%%% perihelion advance of the planet Mercury
%%% could be explained by modifying Newton's law
%%% of gravitation from a $r^{-2}$ dependence to
%%% $r^{-2.000\,000\,157\,4}$. His proposal was
%%% later shown to contradict more accurate
%%% measurements of the orbit of Earth's Moon.
%%% That story is told on pages 93--95 of
%%% Clifford M. Will's 1993 book, ``Was Einstein
%%% Right?'' (ISBN 0-465-09086-9).
%%%
%%% Although many papers purport to explain
%%% Benford's Law, a recent paper (entry
%%% Berger:2011:BLS) argues that several of the
%%% prior published explanations are flawed. An
%%% earlier paper (entry Raimi:1976:FDP) examines
%%% the literature on Benford's Law up to 1976,
%%% and points out flaws in several previous
%%% explanations of the law. That paper also
%%% gives a bibliography of previous important
%%% works on the problem. A recent survey (entry
%%% Berger:2011:BTB) may provide stronger
%%% mathematical grounds for Benford's Law.
%%%
%%% Benford's Law has been applied to the problem
%%% of detection of fraud in data, elections, and
%%% finance (see, among other entries,
%%% Hill:1998:FDP, Nigrini:1992:DIE,
%%% Swanson:2003:DPF, Durtschi:2004:EUB,
%%% Geyer:2004:DFD, Bhattacharya:2005:CPA,
%%% Cleary:2005:ADA, Lu:2005:DFH, Lu:2006:AFD,
%%% Schneider:2006:RAS, Cho:2007:BBL,
%%% Diekmann:2007:FDU, Hand:2007:DDD,
%%% Todter:2009:BLI, Corazza:2010:CFM, and
%%% Roukema:2014:FDA, and the cautionary view in
%%% Diekmann:2010:BLF).
%%%
%%% Benford's Law also applies to floating-point
%%% numbers in computer arithmetic (see entries
%%% Konheim:1965:MDT, Hamming:1970:DN,
%%% Tsao:1974:DSD, Feldstein:1976:CED,
%%% Feldstein:1986:OUS, Schatte:1988:ASC), where
%%% it has implications for the frequency of
%%% significance loss in subtraction of
%%% like-signed numbers.
%%%
%%% This bibliography also includes publications
%%% about two related empirical laws: Heaps' Law
%%% and Zipf's Law, because they often occur in
%%% discussions of Benford's Law.
%%%
%%% Heaps' Law (see entry Heaps:1978:IRC) is an
%%% empirical observation from linguistics that
%%% the proportion of words from a vocabulary
%%% grows exponentially (but with a small
%%% exponent, often between 0.4 and 0.6) with the
%%% number of words in the text of documents.
%%%
%%% Zipf's Law says that if S is some stochastic
%%% (random) variable, the probability that S
%%% exceeds s is proportional to 1 / s. The
%%% variable S might be, for example, the
%%% population of a city (small cities are more
%%% numerous than large ones). Zipf's Law is
%%% a special case of the Pareto distribution
%%% (see remark in entry Pareto:1896:CEP).
%%%
%%% Zipf's law finds application in the design of
%%% information retrieval systems (e.g., hash
%%% tables, databases, filesystems, and Web
%%% searches), as well as in astronomy, biology,
%%% computer science, demography, earth science,
%%% economics, and physics. See entry
%%% Newman:2005:PLP for an outstanding survey
%%% that deserves to be widely read by
%%% scientists, and entry Baldi:2003:MIW for a
%%% book-length treatment.
%%%
%%% There is an actively-maintained bibliography
%%% of Benford's Law at
%%%
%%% http://www.benfordonline.net/
%%%
%%% (see entry Berger:2009:BOB). It includes
%%% material from entries Hurlimann:2006:BLB and
%%% Nigrini:1992:DIE. Although BibTeX output is
%%% mentioned, it may not yet be implemented.
%%%
%%% There is an online bibliography of Zipf's Law
%%% at
%%%
%%% http://www.nslij-genetics.org/wli/zipf/
%%%
%%% (see entry Li:2011:ZLB).
%%%
%%% There is a collection of several papers on
%%% election-fraud detection, some of them using
%%% Benford's Law analyses, at
%%%
%%% http://www-personal.umich.edu/~wmebane/
%%%
%%% At version 1.82, the year coverage looked like
%%% this:
%%%
%%% 1881 ( 1) 1926 ( 1) 1971 ( 2)
%%% 1882 ( 0) 1927 ( 1) 1972 ( 6)
%%% 1883 ( 0) 1928 ( 2) 1973 ( 8)
%%% 1884 ( 0) 1929 ( 1) 1974 ( 11)
%%% 1885 ( 0) 1930 ( 0) 1975 ( 11)
%%% 1886 ( 0) 1931 ( 1) 1976 ( 10)
%%% 1887 ( 0) 1932 ( 2) 1977 ( 6)
%%% 1888 ( 0) 1933 ( 0) 1978 ( 8)
%%% 1889 ( 0) 1934 ( 1) 1979 ( 4)
%%% 1890 ( 0) 1935 ( 1) 1980 ( 8)
%%% 1891 ( 0) 1936 ( 1) 1981 ( 10)
%%% 1892 ( 0) 1937 ( 1) 1982 ( 8)
%%% 1893 ( 0) 1938 ( 2) 1983 ( 6)
%%% 1894 ( 0) 1939 ( 0) 1984 ( 15)
%%% 1895 ( 0) 1940 ( 0) 1985 ( 9)
%%% 1896 ( 1) 1941 ( 0) 1986 ( 10)
%%% 1897 ( 0) 1942 ( 0) 1987 ( 14)
%%% 1898 ( 0) 1943 ( 1) 1988 ( 12)
%%% 1899 ( 0) 1944 ( 1) 1989 ( 13)
%%% 1900 ( 0) 1945 ( 2) 1990 ( 6)
%%% 1901 ( 0) 1946 ( 1) 1991 ( 9)
%%% 1902 ( 0) 1947 ( 0) 1992 ( 11)
%%% 1903 ( 0) 1948 ( 2) 1993 ( 9)
%%% 1904 ( 0) 1949 ( 2) 1994 ( 9)
%%% 1905 ( 0) 1950 ( 3) 1995 ( 15)
%%% 1906 ( 0) 1951 ( 0) 1996 ( 19)
%%% 1907 ( 0) 1952 ( 1) 1997 ( 15)
%%% 1908 ( 0) 1953 ( 1) 1998 ( 17)
%%% 1909 ( 0) 1954 ( 1) 1999 ( 25)
%%% 1910 ( 0) 1955 ( 1) 2000 ( 16)
%%% 1911 ( 0) 1956 ( 0) 2001 ( 25)
%%% 1912 ( 1) 1957 ( 5) 2002 ( 28)
%%% 1913 ( 1) 1958 ( 1) 2003 ( 40)
%%% 1914 ( 1) 1959 ( 1) 2004 ( 41)
%%% 1915 ( 1) 1960 ( 1) 2005 ( 60)
%%% 1916 ( 1) 1961 ( 2) 2006 ( 58)
%%% 1917 ( 1) 1962 ( 2) 2007 ( 42)
%%% 1918 ( 0) 1963 ( 1) 2008 ( 43)
%%% 1919 ( 0) 1964 ( 1) 2009 ( 62)
%%% 1920 ( 1) 1965 ( 4) 2010 ( 83)
%%% 1921 ( 0) 1966 ( 4) 2011 ( 81)
%%% 1922 ( 1) 1967 ( 2) 2012 ( 42)
%%% 1923 ( 0) 1968 ( 4) 2013 ( 22)
%%% 1924 ( 0) 1969 ( 11) 2014 ( 20)
%%% 1925 ( 1) 1970 ( 8) 2015 ( 11)
%%%
%%% Article: 838
%%% Book: 74
%%% InCollection: 31
%%% InProceedings: 40
%%% Manual: 1
%%% MastersThesis: 4
%%% Misc: 16
%%% PhdThesis: 8
%%% Proceedings: 7
%%% TechReport: 46
%%% Unpublished: 3
%%%
%%% Total entries: 1068
%%%
%%% Data for this bibliography have been
%%% collected from
%%%
%%% * the University of Utah Mathematics
%%% Department bibliography archives
%%%
%%% * the TeX User Group bibliography
%%% archives
%%%
%%% * the Karlsruhe Computer Science
%%% bibliography archives
%%%
%%% * the Karlsruhe virtual catalog at
%%% http://www.ubka.uni-karlsruhe.de/kvk_en.html
%%%
%%% * the US Library of Congress catalog at
%%% http://catalog.loc.gov/
%%%
%%% * the author's cattobib utility, which
%%% provides Z39.50 interfaces to many
%%% large libraries around the world, at
%%% http://www.math.utah.edu/pub/cattobib/
%%%
%%% * the American Institute of Physics
%%% Scitation database at
%%% http://scitation.aip.org/search_scitation
%%%
%%% * the American Physical Society PROLA
%%% database at
%%% http://publish.aps.org/search
%%%
%%% * the American Mathematical Society
%%% MathSciNet database at
%%% http://ams.rice.edu/mathscinet/search.html
%%%
%%% * the Bulletin of the Atomic Scientists
%%% (archives available, albeit inconveniently,
%%% via http://books.google.com/ and
%%% http://bos.sagepub.com/search)
%%%
%%% * the Canadian Journal of Physics
%%% database at
%%% http://www.nrcresearchpress.com/search/advanced
%%%
%%% * the European Mathematical Society
%%% Zentralblatt fuer Mathematik database
%%% at http://zb.msri.org/ZMATH/zmath/en/
%%%
%%% * the Europhysics journal archive at
%%% http://www.europhysicsnews.org/
%%%
%%% * the JSTOR database at
%%% http://www.jstor.org/
%%%
%%% * the Nature journal archive at
%%% http://www.nature.com/search/
%%%
%%% * the journal archives of the National
%%% Academy of Science at
%%% http://www.pnas.org/
%%%
%%% * the Project Euclid archives at
%%% http://projecteuclid.org/
%%%
%%% * the SAO/NASA Astrophysics Data System at
%%% http://adsabs.harvard.edu/
%%%
%%% * the Science journal archive at
%%% http://www.sciencemag.org/search
%%%
%%% * the SPIRES high-energy physics
%%% literature database at the Stanford
%%% Linear Accelerator at Stanford
%%% University at
%%% http://www.slac.stanford.edu/spires/hep/search/
%%%
%%% * the Springer journal database at
%%% http://www.springer.com/?SGWID=0-102-13-0-0
%%%
%%% * the Wiley journal database at
%%% http://onlinelibrary.wiley.com/
%%%
%%% * many online library catalogs, including
%%% those of the British Library, the
%%% Karlsruhe Virtual Library catalog, the
%%% Oxford University Library, the University of
%%% California library system, and the US
%%% Library of Congress.
%%%
%%% The checksum field above contains a CRC-16
%%% checksum as the first value, followed by the
%%% equivalent of the standard UNIX wc (word
%%% count) utility output of lines, words, and
%%% characters. This is produced by Robert
%%% Solovay's checksum utility.",
%%% }
%%% ====================================================================
@Preamble{
"\let \k = \c" #
"\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" #
"\ifx \undefined \circled \def \circled #1{(#1)}\fi" #
"\ifx \undefined \cprime \def \cprime{$'$} \fi" #
"\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi" #
"\ifx \undefined \polhk \def \polhk #1{\setbox0=\hbox{#1}{\ooalign{\hidewidth \lower1.5ex\hbox{`}\hidewidth\crcr\unhbox0}}} \fi" #
"\ifx \undefined \reg \def \reg {\circled{R}}\fi" #
"\ifx \undefined \url \input{path.sty} \fi"
}
%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-mjn = "Mark J. Nigrini"}
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|http://www.math.utah.edu/~beebe/|"}
%%% ====================================================================
%%% Journal abbreviations:
@String{j-ACCOUNT-HIST-J = "Accounting Historians Journal"}
@String{j-ACCOUNT-RES = "Accountability in Research"}
@String{j-ACCOUNT-REV = "The Accounting Review"}
@String{j-ACCOUNTANCY = "Accountancy: The journal of the {Institute
of Chartered Accountants in England and
Wales}"}
@String{j-ACTA-ARITHMETICA = "Acta Arithmetica"}
@String{j-ACTA-ASTRONAUT = "Acta Astronautica"}
@String{j-ADV-APPL-STAT = "Advances and Applications in Statistics"}
@String{j-ADV-COMPLEX-SYST = "Advances in Complex Systems"}
@String{j-ADV-MATH = "Advances in Mathematics"}
@String{j-AEQUATIONES-MATHEMATICAE = "Aequationes Mathematicae"}
@String{j-AEROBIOLOGIA = "Aerobiologia"}
@String{j-AM-J-ECON-SOCIOL = "The American Journal of Economics and
Sociology"}
@String{j-AM-J-MATH = "American Journal of Mathematics"}
@String{j-AM-J-MATH-MANAGE-SCI = "American Journal of Mathematical and
Management Sciences"}
@String{j-AM-SCI = "American Scientist"}
@String{j-AMER-J-PHYSICS = "American Journal of Physics"}
@String{j-AMER-J-PSYCHOLOGY = "The American Journal of Psychology"}
@String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"}
@String{j-AMER-STAT = "The American Statistician"}
@String{j-ANALYST = "The Analyst"}
@String{j-ANIM-BEHAV = "Animal Behaviour"}
@String{j-ANN-APPL-PROBAB = "Annals of Applied Probability"}
@String{j-ANN-INST-STAT-MATH-TOKYO = "Annals of the Institute of Statistical
Mathematics (Tokyo)"}
@String{j-ANN-MATH-STAT = "Annals of Mathematical Statistics"}
@String{j-ANN-PROBAB = "Annals of Probability"}
@String{j-ANN-STAT = "Annals of Statistics"}
@String{j-APPL-ECON-LETT = "Applied Economics Letters"}
@String{j-APPL-FINANC-ECON = "Applied Financial Economics"}
@String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"}
@String{j-APPL-STAT = "Applied Statistics"}
@String{j-AQUAT-BOT = "Aquatic Botany"}
@String{j-ASIA-PAC-MATH-NEWSL = "Asia Pacific Mathematics Newsletter"}
@String{j-ASLIB-PROC = "ASLIB Proceedings"}
@String{j-ASTROPART-PHYS = "Astroparticle Physics"}
@String{j-AUDITING = "Auditing: A Journal of Practice \& Theory"}
@String{j-AUSTRALIAN-COMP-J = "Australian Computer Journal"}
@String{j-AUSTRALIAN-MATH-SOC-GAZ = "Australian Mathematical Society Gazette"}
@String{j-BELL-SYST-TECH-J = "The Bell System Technical Journal"}
@String{j-BIOINFORMATICS = "Bioinformatics"}
@String{j-BIOMETRIKA = "Biometrika"}
@String{j-BIOSYSTEMS = "Biosystems (A6E)"}
@String{j-BMC-BIOINFORMATICS = "BMC Bioinformatics"}
@String{j-BRAIN-COGN = "Brain and Cognition"}
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%%% ====================================================================
%%% Series abbreviations:
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%%% ====================================================================
%%% Bibliography entries, sorted by year, and then by citation label:
@Article{Newcomb:1881:NFU,
author = "Simon Newcomb",
title = "Note on the frequency of use of the different digits
in natural numbers",
journal = j-AM-J-MATH,
volume = "4",
number = "1--4",
pages = "39--40",
year = "1881",
CODEN = "AJMAAN",
ISSN = "0002-9327 (print), 1080-6377 (electronic)",
ISSN-L = "0002-9327",
bibdate = "Thu Feb 15 16:35:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/2369148",
abstract = "That the ten digits do not occur with equal frequency
must be evident to any one making much use of
logarithmic tables, and noticing how much faster the
first pages wear out than the last ones. The first
significant figure is oftener 1 than any other digit,
and the frequency diminishes up to 9.",
acknowledgement = ack-nhfb,
author-dates = "March 12, 1835--July 11, 1909",
fjournal = "American Journal of Mathematics",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 40: ``The law of probability of the occurrence
of numbers is such that all mantissas of their
logarithms are equally probable.''. The article
contains no references to earlier work.",
remark-2 = "The papers \cite{Boring:1920:LNL,Raimi:1976:FDP} are
the earliest citations of Newcomb's work that I have
yet found in connection with Benford's Law.",
xxURL = "http://en.wikipedia.org/wiki/Simon_Newcomb",
}
@Book{Pareto:1896:CEP,
author = "Vilfredo Pareto",
title = "Cours d'{\'e}conomie politique profess{\'e} a
l'universit{\'e} de {Lausanne}. (French) [{Course} on
political economy given at the {University of
Lausanne}]",
publisher = "F. Rouge",
address = "Lausanne, Switzerland",
pages = "????",
year = "1896--1897",
LCCN = "HB173 .P22",
bibdate = "Wed Nov 16 08:41:03 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "French",
remark = "Two volumes issued in successive years. The Italian
economist and mathematician, Vilfredo Federico (born in
Paris, France, and initially named Wilfried Fritz)
Pareto (15 July 1848--19 August 1923), introduced the
80--20 rule in economics (80\% of the wealth is owned
by 20\% of the people, which was true at the time in
Italy, and found to be similar in other countries). He
developed the Pareto distribution, in which a random
variable $X$ has the property that the probability that
it is greater than some number $x$ is given by $ {\rm
Pr}(X > x) = (x_m / x)^\alpha $ for $ x > x_m $, and $
{\rm Pr}(X > x) = 1 $ otherwise. The positive value $
x_m $ is a cutoff, and as $ \alpha \to \infty $, the
Pareto distribution approaches a Dirac delta function,
$ \delta (x - x_m) $. When this models the distribution
of wealth, the exponent $ \alpha $ is called the {\em
Pareto index}.",
}
@Book{Poincare:1912:CPL,
author = "H. Poincar{\'e}",
title = "Calcul des Probabilit{\'e}s: Le{\c{c}}ons
profess{\'e}es pendant le deuxi{\`e} me semestre
1893--1894. ({French}) [{Calculation} of Probabilities:
Lectures from the second semester 1893--1894]",
publisher = "Gauthier-Villars",
address = "Paris, France",
pages = "ii + 274",
year = "1912",
LCCN = "QA273 .P75",
bibdate = "Mon Nov 14 10:08:18 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
author-dates = "1854--1912",
language = "French",
remark = "See pp. 313--320.",
}
@Article{Auerbach:1913:GBG,
author = "Felix Auerbach",
title = "{Das Gesetz der Bev{\"o}lkerungskonzentration}.
({German}) [{The} law of population concentration]",
journal = "{Petermann's Geographische Mitteilungen}",
volume = "59",
number = "1",
pages = "74--76",
month = "????",
year = "1913",
CODEN = "PGGMA3",
ISSN = "0031-6229",
ISSN-L = "0031-6229",
bibdate = "Thu Nov 24 10:49:06 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This paper is reported in \cite{Newman:2005:PLP} to be
the first discovery of {\em Zipf's Law\/} in connection
with city populations (see \cite{Zipf:1932:SSP}). See
also \cite{Estoup:1916:GSM}.",
URL = "http://hdl.handle.net/2027/mdp.39015035583528?urlappend=%3Bseq=122",
acknowledgement = ack-nhfb,
ajournal = "Petermanns Geogr. Mitteilung",
ajournal-2 = "Petermanns Geogr. Mitt.",
language = "German",
}
@Article{Stamp:1914:NIP,
author = "J. C. Stamp",
title = "A New Illustration of {Pareto}'s Law",
journal = j-J-R-STAT-SOC,
volume = "77",
number = "2",
pages = "200--204",
month = jan,
year = "1914",
DOI = "http://dx.doi.org/10.2307/2339802",
ISSN = "0952-8385",
bibdate = "Sat Jan 24 11:18:04 MST 2015",
bibsource = "http://www.jstor.org/stable/i315805;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-a-1910.bib",
URL = "http://www.jstor.org/stable/2339802",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society",
}
@Article{Weyl:1915:GZM,
author = "Hermann Weyl",
title = "{{\"U}ber die Gleichverteilung von Zahlen mod. Eins}.
({German}) [{On} the uniform distribution of numbers
mod. one]",
journal = j-MATH-ANN,
volume = "77",
number = "3",
pages = "313--352",
month = "????",
year = "1915",
CODEN = "MAANA3",
DOI = "http://dx.doi.org/10.1007/BF01475864",
ISSN = "0025-5831 (print), 1432-1807 (electronic)",
ISSN-L = "0025-5831",
bibdate = "Sun Nov 13 10:54:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Ann.",
fjournal = "Mathematische Annalen",
language = "German",
xxyear = "1916",
}
@Book{Estoup:1916:GSM,
author = "J. B. Estoup",
title = "Gammes St{\'e}nographiques: m{\'e}thode \& exercices
pour l'acquisition de la vitesse ({French})
[Stenographic ranges: method and exercises for
achieving speed]",
publisher = "Institut St{\'e}nographique de France",
address = "Paris, France",
edition = "Fourth",
pages = "151",
year = "1916",
LCCN = "????",
bibdate = "Thu Nov 24 14:24:28 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This on shorthand writing is the earliest known
publication of the power-law distribution of word
frequencies, generally credited to
\cite{Zipf:1932:SSP}.",
acknowledgement = ack-nhfb,
keywords = "Zipf's Law",
language = "French",
}
@Article{Franel:1917:PTL,
author = "J. Franel",
title = "{{\`A}} propos des tables de logarithmes. ({French})
[{On} tables of logarithms]",
journal = "Festschrift Naturforschenden der Gesellschaft in
Z{\"u}rich Vierteljahrsschrift",
volume = "62",
number = "??",
pages = "286--295",
month = "????",
year = "1917",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 10:09:40 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "French",
}
@Article{Boring:1920:LNL,
author = "Edwin G. Boring",
title = "The Logic of the Normal Law of Error in Mental
Measurement",
journal = j-AMER-J-PSYCHOLOGY,
volume = "31",
number = "1",
pages = "1--33",
month = jan,
year = "1920",
CODEN = "AJPCAA",
ISSN = "0002-9556 (print), 1939-8298 (electronic)",
ISSN-L = "0002-9556",
bibdate = "Thu Dec 01 21:35:43 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/1413989",
acknowledgement = ack-nhfb,
fjournal = "The American journal of psychology",
remark = "A citation search in Google Scholar on 1-Dec-2011
found this article as the only one citing Newcomb's
work \cite{Newcomb:1881:NFU} before it was brought to
wider view by Raimi's frequently-cited paper
\cite{Raimi:1976:FDP}. Boring's article has only brief
mention of Newcomb's work, and then solely in
connection with the believed randomness of digits of
transcendental numbers.",
}
@InCollection{Macaulay:1922:PLG,
author = "F. R. Macaulay",
editor = "W. C. Mitchell",
booktitle = "Income in the {United States}: Its Amount and
Distribution: 1909--1919",
title = "{Pareto}'s law and the general problem of mathematical
describing the frequency of distribution of income",
publisher = "National Bureau of Economic Research",
address = "New York, NY, USA",
pages = "??--??",
year = "1922",
LCCN = "????",
bibdate = "Fri Nov 25 09:06:43 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Yule:1925:MTE,
author = "G. Udny Yule",
title = "A Mathematical Theory of Evolution, Based on the
Conclusions of {Dr. J. C. Willis, F.R.S.}",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-B-BIO-SCI,
volume = "213",
number = "??",
pages = "21--87",
day = "14",
month = may,
year = "1925",
CODEN = "PTRBAE",
DOI = "http://dx.doi.org/10.1098/rstb.1925.0002",
ISSN = "0962-8436",
ISSN-L = "0962-8436",
bibdate = "Tue Nov 15 10:45:15 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://rstb.royalsocietypublishing.org/content/213/402-410/21",
acknowledgement = ack-nhfb,
fjournal = "Philosophical transactions of the Royal Society of
London Series B, Biological sciences",
}
@Article{Lotka:1926:FDS,
author = "Alfred J. Lotka",
title = "The Frequency Distribution of Scientific
Productivity",
journal = j-J-WASH-ACAD-SCI,
volume = "16",
number = "12",
pages = "317--323",
month = dec,
year = "1926",
CODEN = "JWASA3",
ISSN = "0043-0439",
ISSN-L = "0043-0439",
bibdate = "Thu Nov 24 14:36:11 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This is the earliest known publication on the
phenomenon known as Zipf's Law, here applied to
publication counts of chemists and physicists. Lotka's
Law (a term possibly first used in
\cite{Zipf:1949:HBP}) says that the number of authors
producing $n$ publications is about $ 1 / n^2 $ of the
number producing only one. This `law' seems to have
been misunderstood and misapplied in other fields; see
\cite{Potter:1981:LLR}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Washington Academy of Sciences",
keywords = "Lotka's Law",
}
@Article{Yule:1927:RS,
author = "G. Udny Yule",
title = "On Reading a Scale",
journal = j-J-R-STAT-SOC,
volume = "90",
number = "3",
pages = "570--587",
month = "????",
year = "1927",
ISSN = "0952-8385",
ISSN-L = "0952-8385",
bibdate = "Wed Nov 23 12:29:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See related later work \cite{Preece:1981:DFD}.",
URL = "http://www.jstor.org/stable/2341205",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society",
remark = "This paper reports on human bias in the recording of
last digits in measurements, or from roundings, or from
later scale conversions.",
}
@Article{Condon:1928:SV,
author = "E. U. Condon",
title = "Statistics of vocabulary",
journal = j-SCIENCE,
volume = "67",
number = "1733",
pages = "300--??",
day = "16",
month = mar,
year = "1928",
CODEN = "SCIEAS",
DOI = "http://dx.doi.org/10.1126/science.67.1733.300",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Fri Nov 25 09:04:50 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Science",
journal-URL = "http://www.sciencemag.org/archive/",
}
@Article{Sun:1928:EFD,
author = "C. P. Sun",
title = "On the Examination of Final Digits by Experiments in
Artificial Sampling",
journal = j-BIOMETRIKA,
volume = "20A",
number = "1/2",
pages = "64--68",
month = jul,
year = "1928",
CODEN = "BIOKAX",
DOI = "http://dx.doi.org/10.2307/2331941",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
bibdate = "Sat Jun 21 13:38:07 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315380;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/biometrika1920.bib",
URL = "http://www.jstor.org/stable/2331941",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://www.jstor.org/journals/00063444.html",
}
@Article{Zipf:1929:RFD,
author = "George Kingsley Zipf",
title = "Relative frequency as a determinant of phonetic
change",
journal = "Harvard Studies in Classical Philology",
volume = "40",
number = "??",
pages = "1--95",
month = "????",
year = "1929",
CODEN = "????",
ISSN = "0073-0688",
ISSN-L = "0073-0688",
bibdate = "Fri Nov 25 09:02:14 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/journals/00730688.html;
http://www.jstor.org/stable/310585",
acknowledgement = ack-nhfb,
}
@Book{Gibrat:1931:IE,
author = "Robert Gibrat",
title = "Les In{\'e}galit{\'e}s {\'e}conomiques",
publisher = "Librairie du Recueil Sirey",
address = "Paris, France",
pages = "286",
year = "1931",
LCCN = "HB251.GIB",
bibdate = "Mon Feb 18 14:43:11 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
library.ox.ac.uk:210/ADVANCE",
note = "Applications: aux in{\'e}galit{\'e}s des richesses,
{\`a} la concentration des entreprises, aux populations
des villes, aux statistiques des familles, etc. d'une
loi nouvelle. La loi de l'effet proportionnel.",
URL = "http://en.wikipedia.org/wiki/Gibrat%27s_law",
acknowledgement = ack-nhfb,
author-dates = "1904--1980",
remark-1 = "According to at least one library catalog (SWB), this
book may be the author's doctoral dissertation from
l'Universit{\'e} de Paris in 1931.",
remark-2 = "This book is cited as the origin of Gibrat's Law, or
Gibrat's rule of proportionate growth, that ``the size
of a firm and its growth rate are independent''.",
}
@Misc{Anonymous:1932:FL,
author = "Anonymous",
title = "Fishpole Lamp",
howpublished = "Web site",
day = "30",
month = apr,
year = "1932",
bibdate = "Sat Feb 23 14:52:20 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This Web site reports that General Electric researcher
Frank Benford invented the electric light pointer, the
forerunner of the modern laser pointer.",
URL = "http://scienceservice.si.edu/pages/012020.htm",
acknowledgement = ack-nhfb,
remark = "CD 2478048, E\&MP12.020, Electric Appliances \
Apparatus.",
}
@Book{Zipf:1932:SSP,
author = "George Kingsley Zipf",
title = "Selected studies of the principle of relative
frequency in language",
publisher = pub-HARVARD,
address = pub-HARVARD:adr,
pages = "51",
year = "1932",
LCCN = "P123 .Z5",
bibdate = "Wed Nov 16 09:03:46 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This book is the origin of {\em Zipf's Law}, but the
phenomenon was apparently first reported two decades
earlier in \cite{Auerbach:1913:GBG} for city
populations, in \cite{Estoup:1916:GSM} for word
frequencies, and in \cite{Lotka:1926:FDS} for
researcher publication counts.",
acknowledgement = ack-nhfb,
author-dates = "1902--1950",
subject = "Plautus, Titus Maccius; language and languages;
semantics; comparative linguistics; Chinese language;
phonology; Latin language; glossaries, vocabularies,
etc; dialects; China; Beijing",
}
@Article{Bradford:1934:SIS,
author = "Samuel C. Bradford",
title = "Sources of Information on Specific Subjects",
journal = "Engineering: An Illustrated Weekly Journal (London)",
volume = "137",
number = "??",
pages = "85--86",
day = "26",
month = jan,
year = "1934",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Nov 25 11:47:10 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This paper (reprinted in \cite{Bradford:1985:SIS})
introduces an observation later known as Bradford's
Law: there are exponentially-diminishing returns of
extending a search for references in journals.",
URL = "http://en.wikipedia.org/wiki/Bradford%27s_law",
acknowledgement = ack-nhfb,
}
@Book{Zipf:1935:PBL,
author = "George Kingsley Zipf",
title = "The psycho-biology of language: an introduction to
dynamic philology",
publisher = pub-HOUGHTON-MIFFLIN,
address = pub-HOUGHTON-MIFFLIN:adr,
pages = "ix + 336",
year = "1935",
LCCN = "P105 .Z5",
bibdate = "Wed Nov 16 09:07:09 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
prodorbis.library.yale.edu:7090/voyager",
acknowledgement = ack-nhfb,
author-dates = "1902--1950",
subject = "language and languages; semantics; comparative
linguistics",
}
@Book{Moon:1936:SBI,
author = "Parry Moon",
title = "The Scientific Basis of Illuminating Engineering",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xi + 608",
year = "1936",
LCCN = "TH7703 .M65",
bibdate = "Mon Nov 14 10:11:54 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
remark = "See pages 420ff.",
}
@Article{Bresciani-Turroni:1937:PL,
author = "C. Bresciani-Turroni",
title = "On {Pareto}'s Law",
journal = j-J-R-STAT-SOC,
volume = "100",
number = "3",
pages = "421--432",
month = "????",
year = "1937",
DOI = "http://dx.doi.org/10.2307/2980528",
ISSN = "0952-8385",
bibdate = "Sat Jan 24 11:18:08 MST 2015",
bibsource = "http://www.jstor.org/stable/i349533;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
URL = "http://www.jstor.org/stable/2980528",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society",
}
@Article{Benford:1938:LAN,
author = "Frank Benford",
title = "The Law of Anomalous Numbers",
journal = j-PROC-AMER-PHIL-SOC,
volume = "78",
number = "4",
pages = "551--572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003-049X",
ISSN-L = "0003-049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
note = "See comments about Benford's biased rounding practices
\cite{Diaconis:1979:RP}.",
URL = "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
ZMnumber = "JFM 64.0555.03; Zbl 0018.26502",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the last
pages, indicating that more used numbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution law---hence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multi-digit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = ack-nhfb,
author-dates = "1883--December 4, 1948",
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573--585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
xxURL = "http://en.wikipedia.org/wiki/Frank_Benford",
}
@Article{Bethe:1938:MSE,
author = "H. A. Bethe and M. E. Rose and L. P. Smith",
title = "The Multiple Scattering of Electrons",
journal = j-PROC-AMER-PHIL-SOC,
volume = "78",
number = "4",
pages = "573--585",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003-049X",
ISSN-L = "0003-049X",
bibdate = "Wed Nov 23 14:27:52 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This paper, which immediately follows Benford's
\cite{Benford:1938:LAN} in this journal issue, is
reported in \cite[p. 197]{Logan:1978:FDP} to have been
of considerable interest to scientists involved in
secret nuclear physics work in World War II. That is
how Benford's paper ``in a journal of rather limited
circulation and not usually read by mathematicians''
came to be noticed by physicists.",
URL = "http://www.jstor.org/stable/984803",
acknowledgement = ack-nhfb,
author-dates = "Hans Albrecht Bethe (1906--2005)",
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
remark = "Biography supplement in \cite{Lee:2007:HAB} has this
as Proc. Am. Philos. Soc., 89, 373--383 (1938), but
that seems to be wrong: check??",
}
@Article{Benford:1943:PAG,
author = "Frank Benford",
title = "The Probable Accuracy of the General Physical
Constants",
journal = j-PHYS-REV,
volume = "63",
number = "5--6",
pages = "212--212",
month = mar,
year = "1943",
CODEN = "PHRVAO",
DOI = "http://dx.doi.org/10.1103/PhysRev.63.212",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
bibdate = "Mon Nov 21 21:52:58 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRev.63.212",
acknowledgement = ack-nhfb,
fjournal = "Physical Review",
journal-URL = "http://prola.aps.org/browse/PR",
}
@Article{Goudsmit:1944:SFN,
author = "S. A. Goudsmit and W. H. Furry",
title = "Significant Figures of Numbers in Statistical Tables",
journal = j-NATURE,
volume = "154",
number = "3921",
pages = "800--801",
day = "23",
month = dec,
year = "1944",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/154800a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See later work \cite{Logan:1978:FDP}, and severe
criticism \cite{Raimi:1976:FDP,Raimi:1985:FDP}.",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = ack-nhfb,
author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
the concept of electron spin, a critical step forward
in the quantum mechanics of many-electron systems.
Surprisingly, that work did not get them the Nobel
Prize, but it did spur Wolfgang Pauli to present his
Exclusion Principle in 1925, for which he received the
1945 Nobel Prize in Physics. After World War II,
Goudsmit was the scientific head of the Alsos mission
to capture German nuclear scientists. In the 1950s, he
founded the journal Physical Review Letters. During the
1960s and 1970s, he was Editor-in-Chief of the main
American physics journal, the Physical Review.",
}
@Article{Furry:1945:DND,
author = "W. H. Furry and Henry Hurwitz",
title = "Distribution of Numbers and Distribution of
Significant Figures",
journal = j-NATURE,
volume = "155",
number = "3924",
pages = "52--53",
day = "13",
month = jan,
year = "1945",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/155052a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Unpublished{Stigler:1945:DLD,
author = "George J. Stigler",
title = "The distribution of leading digits in statistical
tables",
year = "1945",
bibdate = "Sat Nov 12 16:07:40 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Unpublished, but written about 1945--1946, and
presented in an 1975 address at Haskell Hall,
University of Chicago. Stigler's distribution is more
complex than that of Newcomb and Benford. Stigler has $
F_d = (d \ln (d) - (d + 1) \ln (d + 1) + (1 + (10 / 9)
\ln (10))) / 9 $, which gives leading-digit frequencies
of 0.2413, 0.1832, 0.1455, 0.1174, 0.0950, 0.0764,
0.0605, 0.0465, and 0.0342. See \cite{Lee:2010:SAR} for
a comparison of the Benford and Stigler distributions,
and their relations to Zipf and Pareto distributions.
For derivations of Stigler's distribution, see
\cite{Logan:1978:FDP,Raimi:1985:FDP}.",
URL = "http://www.nobelprize.org/nobel_prizes/economics/laureates/1982/",
acknowledgement = ack-nhfb,
remark = "Stigler won the 1982 Sveriges Riksbank Prize in
Economic Sciences in Memory of Alfred Nobel (often
called the Nobel Prize in Economics, although that
field was not among the original ones funded by Nobel's
will).",
}
@Book{Furlan:1946:HSU,
author = "Luigi Vladimir Furlan",
title = "{Das Harmoniegesetz der Statistik: Eine Untersuchung
{\"u}ber die metrische Interdependenz der sozialen
Erscheinungen}. ({German}) [{The} {Law of Harmony} in
statistics: an investigation of the metrical
interdependence of social phenomena]",
volume = "2",
publisher = "Verlag f{\"u}r Recht und Gesellschaft A.-G.",
address = "Basel, Switzerland",
pages = "xii + 504",
year = "1946",
LCCN = "HA29 .F85",
bibdate = "Mon Nov 14 09:40:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "{Beihefte zum Assekuranzjahrbuch}",
acknowledgement = ack-nhfb,
author-dates = "1886--",
keywords = "Benford--Furlan Law",
language = "German",
}
@Article{Geiringer:1948:RVF,
author = "Hilda Geiringer",
title = "Review of {L. V. Furlan}'s book: {Das Harmoniegesetz
der Statistik: Eine Untersuchung {\"u}ber die metrische
Interdependenz der sozialen Erscheinungen}. ({German})
[{The} {Law of Harmony} in statistics: an investigation
of the metrical interdependence of social phenomena]",
journal = j-J-AM-STAT-ASSOC,
volume = "43",
number = "242",
pages = "325--328",
month = jun,
year = "1948",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Mon Nov 14 09:42:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
note = "See \cite{Furlan:1946:HSU}.",
URL = "http://www.jstor.org/stable/2280379",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Hsu:1948:ESM,
author = "E. H. Hs{\"u}",
title = "An Experimental Study on ``Mental Numbers'' and a New
Application",
journal = j-J-GEN-PSYCH,
volume = "38",
number = "1",
pages = "57--67",
month = "????",
year = "1948",
CODEN = "JGPSAY",
DOI = "http://dx.doi.org/10.1080/00221309.1948.9711768",
ISSN = "0022-1309 (print), 1940-0888 (electronic)",
ISSN-L = "0022-1309",
bibdate = "Sat Jan 07 09:29:53 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00221309.1948.9711768",
acknowledgement = ack-nhfb,
fjournal = "The Journal of General Psychology",
keywords = "Benford's Law",
onlinedate = "06 Jul 2010",
}
@Book{Hardy:1949:DS,
author = "G. H. (Godfrey Harold) Hardy",
title = "Divergent series",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xvi + 396",
year = "1949",
LCCN = "QA295 .H29",
bibdate = "Wed Nov 16 08:14:50 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1877--1947",
}
@Book{Zipf:1949:HBP,
author = "George Kingsley Zipf",
title = "Human behaviour and the principle of least effort",
publisher = "Hafner Pub. Co.",
address = "New York, NY, USA",
pages = "xi + 573",
year = "1949",
LCCN = "H91 .Z5 1949a",
bibdate = "Tue Nov 15 09:35:14 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1902--1950",
remark = "Reprinted 1965.",
subject = "Human ecology",
}
@Article{Anonymous:1950:BRZ,
author = "Anonymous",
title = "Book review: {Zipf, George K., \booktitle{Human
behavior and the principle of least effort}. Cambridge,
(Mass.): Addison-Wesley, 1949, pp. 573}",
journal = j-J-CLIN-PSYCHOL,
volume = "6",
number = "3",
pages = "306--306",
year = "1950",
CODEN = "JCPYAO",
DOI = "2-7;
http://dx.doi.org/10.1002/1097-4679(195007)6:3<306::AID-JCLP2270060331>3.0.CO",
ISSN = "0021-9762 (print), 1097-4679 (electronic)",
ISSN-L = "0021-9762",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Clinical Psychology",
}
@Book{Feller:1950:IPT,
author = "William Feller",
title = "Introduction to Probability Theory",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "????",
year = "1950",
LCCN = "QA273 .F37",
bibdate = "Mon Nov 14 09:57:35 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Wiley series in probability and mathematical
statistics. Probability and mathematical statistics",
acknowledgement = ack-nhfb,
author-dates = "William Feller (1906--1970)",
}
@Article{Macon:1950:DFD,
author = "N. Macon and L. Moser",
title = "On the distribution of first digits of powers",
journal = "Scripta Mathematica",
volume = "16",
number = "??",
pages = "290--291",
month = "????",
year = "1950",
CODEN = "????",
ISSN = "0036-9713",
ISSN-L = "0036-9713",
bibdate = "Sat Nov 12 16:28:13 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica",
}
@Article{Tsuji:1952:UDN,
author = "M. Tsuji",
title = "On the uniform distribution of numbers $ \bmod 1 $",
journal = j-J-MATH-SOC-JPN,
volume = "4",
number = "3--4",
pages = "313--322",
month = "????",
year = "1952",
CODEN = "NISUBC",
DOI = "http://dx.doi.org/10.2969/jmsj/00430313",
ISSN = "0025-5645",
ISSN-L = "0025-5645",
bibdate = "Sun Feb 17 06:33:32 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/euclid.jmsj/1261415780",
acknowledgement = ack-nhfb,
fjournal = "Journal of the {Mathematical Society of Japan}",
}
@InProceedings{Mandelbrot:1953:ITS,
author = "Beno{\^\i}t B. Mandelbrot",
editor = "Willis Jackson",
booktitle = "{Communication theory: papers read at a Symposium on
``Applications of Communication Theory'' held at the
Institution of Electrical Engineers, London, September
22nd--26th 1952}",
title = "An Informational Theory of the Statistical Structure
of Languages",
publisher = pub-BUTTERWORTHS,
address = pub-BUTTERWORTHS:adr,
pages = "486--502",
year = "1953",
LCCN = "Q350 .S92 1952",
bibdate = "Wed Nov 16 09:37:30 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://lccn.loc.gov/53004215;
http://www.nytimes.com/2010/10/17/us/17mandelbrot.html",
acknowledgement = ack-nhfb,
bookpages = "xii + 532",
remark = "The paper is incorrectly referenced as a book in
\cite{Baek:2011:ZLU}. Mandelbrot got his Master of
Science in Aeronautics at CalTech in 1948, and his
Docteur d'{\'E}tat {\`e}s Sciences Math{\'e}matiques in
1952 in Paris, so perhaps this is a translation of his
thesis work.",
}
@Book{Blackwell:1954:TGS,
author = "David Blackwell and Meyer A. Girshick",
title = "Theory of Games and Statistical Decisions",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xi + 355",
year = "1954",
LCCN = "QA269 .B5",
bibdate = "Mon Nov 14 10:04:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://catalog.hathitrust.org/Record/000577721",
acknowledgement = ack-nhfb,
author-dates = "David Blackwell (1919--2010)",
keywords = "Benford's Law",
remark = "Brief mention of Benford's Law on page 74, problem
2.7.2 (??).",
}
@Article{Simon:1955:CSD,
author = "Herbert A. Simon",
title = "On a Class of Skew Distribution Functions",
journal = j-BIOMETRIKA,
volume = "42",
number = "3/4",
pages = "425--440",
month = dec,
year = "1955",
CODEN = "BIOKAX",
DOI = "http://dx.doi.org/10.2307/2333389",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
MRclass = "62.0X",
MRnumber = "0073085 (17,380e)",
MRreviewer = "H. A. David",
bibdate = "Sat Jun 21 14:32:48 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315425;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/biometrika1950.bib",
URL = "http://www.jstor.org/stable/2333389",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://biomet.oxfordjournals.org/content/by/year;
http://www.jstor.org/journals/00063444.html",
keywords = "distribution of income; distribution of species among
genera; distributions of city populations;
distributions of document word frequencies;
distributions of scientific publication counts; Zipf's
Law",
remark = "This work is an extension of Yule's work
\cite{Yule:1925:MTE}. See discussion
\cite{Mandelbrot:1959:NCS} and comments
\cite{Mitzenmacher:2003:BHG}.",
}
@Article{Devooght:1957:LZM,
author = "J. Devooght",
title = "Sur la loi de {Zipf--Mandelbrot}. ({French}) [On the
{Zipf--Mandelbrot} law]",
journal = "Acad. Roy. Belg. Bull. Cl. Sci. (5)",
volume = "43",
pages = "244--251",
year = "1957",
CODEN = "????",
ISSN = "0001-4141",
ISSN-L = "0001-4141",
MRclass = "94.0X",
MRnumber = "0088412 (19,516a)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Acad{\'e}mie Royale de Belgique. Bulletin de la Classe
des Sciences. Koninklijke Belgische Academie.
Mededelingen van de Klasse der Wetenschappen. 5e
S{\'e}rie",
language = "French",
}
@Book{Feller:1957:IPT,
author = "William Feller",
title = "Introduction to Probability Theory",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "461 (vol. 1), 626 (vol. 2)",
year = "1957",
LCCN = "QA273 .F3712",
bibdate = "Mon Nov 14 09:57:35 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://catdir.loc.gov/catdir/toc/onix01/57010805.html",
acknowledgement = ack-nhfb,
author-dates = "William Feller (1906--1970)",
}
@Article{Gini:1957:SFD,
author = "Corrado Gini",
title = "Sulla frequenza delle cifre iniziali dei numeri
osservati. ({Italian}) [{On} the frequency of initial
digits of observed numbers]",
journal = "{Bulletin de l'Institut International de
Statistique}",
volume = "35",
number = "2",
pages = "57--76",
year = "1957",
CODEN = "BISQA3",
ISSN = "????",
MRclass = "62.00",
MRnumber = "0117807 (22 \#8581)",
bibdate = "Sun Sep 18 11:54:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "29th session, 2nd delivery, Rio de Janerio.",
acknowledgement = ack-nhfb,
ajournal = "Bull. Inst. Internat. Stat.",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
xxvolume = "34 (wrong!)",
}
@Article{Herzel:1957:SDD,
author = "Amato Herzel",
title = "Sulla distribuzione della cifre iniziali dei numeri
statistici. ({Italian}) [{On} the frequency of initial
digits of statistical numbers]",
journal = "{Atti dell XV e XVII Riunione, Societa Italiana di
Statistica}",
volume = "??",
number = "??",
pages = "205--228",
year = "1957",
CODEN = "????",
ISSN = "????",
bibdate = "Sun Sep 18 12:00:07 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
}
@Article{Miller:1957:SEI,
author = "George A. Miller",
title = "Some Effects of Intermittent Silence",
journal = j-AMER-J-PSYCHOLOGY,
volume = "70",
number = "2",
pages = "311--314",
month = jun,
year = "1957",
CODEN = "AJPCAA",
ISSN = "0002-9556 (print), 1939-8298 (electronic)",
ISSN-L = "0002-9556",
bibdate = "Tue Nov 15 09:40:05 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/1419346",
acknowledgement = ack-nhfb,
fjournal = "The American Journal of Psychology",
keywords = "Zipf's Law",
}
@Book{Zeller:1958:TLG,
author = "Karl Zeller",
title = "{Theorie der Limitierungsverfahren}. (German)
[{Theory} of limiting processes]",
volume = "15",
publisher = pub-SV,
address = pub-SV:adr,
pages = "242",
year = "1958",
LCCN = "QA295 .Z4",
bibdate = "Wed Nov 16 06:43:43 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "{Ergebnisse der Mathematik und ihrer Grenzgebiete}",
acknowledgement = ack-nhfb,
language = "German",
subject = "series; convergence",
}
@Article{Mandelbrot:1959:NCS,
author = "Beno{\^\i}t Mandelbrot",
title = "A note on a class of skew distribution functions:
analysis and critique of a paper by {H. A. Simon}",
journal = j-INF-CONTROL,
volume = "2",
number = "??",
pages = "90--99",
month = apr,
year = "1959",
CODEN = "IFCNA4",
DOI = "http://dx.doi.org/10.1016/S0019-9958(59)90098-1",
ISSN = "0019-9958 (print), 1878-2981 (electronic)",
ISSN-L = "0019-9958",
bibdate = "Wed Nov 16 09:45:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Simon:1955:CSD}.",
abstract = "This note is a discussion of H. A. Simon's model
(1955) concerning the class of frequency distributions
generally associated with the name of G. K. Zipf. The
main purpose is to show that Simon's model is
analytically circular in the case of the linguistic
laws of Estoup--Zipf and Willis--Yule. Insofar as the
economic law of Pareto is concerned, Simon has himself
noted that his model is a particular case of that of
Champernowne; this is correct, with some reservation. A
simplified version of Simon's model is included.",
acknowledgement = ack-nhfb,
fjournal = "Information and Control",
}
@Article{Mandelbrot:1960:PLL,
author = "Beno{\^\i}t Mandelbrot",
title = "The {Pareto--Levy} law and the distribution of
income",
journal = j-INT-ECON-REV,
volume = "1",
number = "??",
pages = "79--106",
month = "????",
year = "1960",
CODEN = "INERAE",
ISSN = "0020-6598 (print), 1468-2354 (electronic)",
ISSN-L = "0020-6598",
bibdate = "Wed Nov 23 11:07:01 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.ingenta.com/journals/browse/bpl/iere",
acknowledgement = ack-nhfb,
fjournal = "International Economic Review",
}
@Article{Cigler:1961:NET,
author = "J. Cigler and G. Helmberg",
title = "{Neuere Entwicklungen der Theorie der
Gleichverteilung}. ({German}) [{Recent} developments in
the theory of uniform distribution]",
journal = j-DEUTSCH-MATH-V,
volume = "64",
number = "??",
pages = "1--50",
month = "????",
year = "1961",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Nov 12 16:33:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Jber. Deutsch. Math.--Verein",
language = "German",
}
@Article{Pinkham:1961:DFS,
author = "Roger S. Pinkham",
title = "On the Distribution of First Significant Digits",
journal = j-ANN-MATH-STAT,
volume = "32",
number = "4",
pages = "1223--1230",
month = dec,
year = "1961",
CODEN = "AASTAD",
ISSN = "0003-4851",
ISSN-L = "0003-4851",
bibdate = "Sat Sep 17 10:19:00 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2237922",
abstract = "It has been noticed by astute observers that well used
tables of logarithms are invariably dirtier at the
front than at the back. Upon reflection one is led to
inquire whether there are more physical constants with
low order first significant digits than high. Actual
counts by Benford [2] show that not only is this the
case but that it seems to be an empirical truth that
whenever one has a large body of physical data,
Farmer's Almanac, Census Reports, Chemical Rubber
Handbook, etc., the proportion of these data with first
significant digit $n$ or less is approximately $
\log_{10}(n + 1) $. Any reader formerly unaware of this
``peculiarity'' will find an actual sampling experiment
wondrously tantalizing. Thus, for example,
approximately $ 0.7 $ of the physical constants in the
Chemical Rubber Handbook begin with $4$ or less ($
\log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted
with the widespread intuitive evaluation $ 4 / 9 $
ths.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 1223: ``\ldots{} the proportion of these data
with first significant digit $n$ or less is
approximately $ \log_{10}(n + 1) $.''\par
\ldots{} ``The only distribution for first significant
digits which is invariant under scale change of the
underlying distribution is $ \log_{10}(n + 1) $.
Contrary to suspicion this is a non-trivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of round-off in computing machines. Since $ d(u v) = u
d v + v d u $, the error resulting from multiplying two
rounded numbers will be governed primarily by the first
significant digits of the two numbers being multiplied.
Now the distribution of first significant digits,
favoring as it does low order digits, tends to produce
less error than would be the case if first significant
digits were uniform as has sometimes been
assumed.''\par
Cited in \cite{Sterbenz:1974:FPC}.",
}
@Book{Hamming:1962:NMS,
author = "R. W. (Richard Wesley) Hamming",
title = "Numerical methods for scientists and engineers",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "411",
year = "1962",
LCCN = "QA297 .H28",
bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis; Electronic digital computers",
}
@TechReport{Mandelbrot:1962:SNR,
author = "Beno{\^\i}t Mandelbrot",
title = "Statistics of natural resources and the law of
{Pareto}",
type = "Research Note",
number = "NC-146",
institution = "IBM",
address = "Yorktown Heights, NY, USA",
day = "29",
month = jun,
year = "1962",
bibdate = "Mon Sep 10 17:35:59 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Book{Weaver:1963:LLT,
author = "Warren Weaver",
title = "{Lady Luck}: The Theory of Probability",
publisher = "Doubleday Anchor Series",
address = "New York, NY, USA",
pages = "392",
year = "1963",
LCCN = "QA273 .W4",
bibdate = "Mon Nov 14 09:54:47 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Benford's Law is discussed on pp. 270--277.",
acknowledgement = ack-nhfb,
author-dates = "Warren, Weaver (1894--1978)",
remark = "Reprinted in \cite{Weaver:1982:LLT}.",
}
@Article{Cigler:1964:MSU,
author = "J. Cigler",
title = "Methods of summability and uniform distribution $
\bmod 1 $",
journal = j-COMPOS-MATH,
volume = "16",
number = "??",
pages = "44--51",
year = "1964",
CODEN = "CMPMAF",
ISSN = "0010-437X (print), 1570-5846 (electronic)",
ISSN-L = "0010-437X",
bibdate = "Mon Nov 14 10:15:31 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Compositio Mathematica",
}
@Article{Good:1965:LE,
author = "I. J. Good",
title = "Letter to the Editor",
journal = j-AMER-STAT,
volume = "19",
number = "3",
pages = "43--43",
month = jun,
year = "1965",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Mon Nov 14 09:56:33 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2681423",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
keywords = "Benford's Law",
remark = "Refers to \cite{Pinkham:1961:DFS}, and cites a review
of that article published by Good in Mathematical
Reviews (1962), page 214, which I have not yet been
able to locate.",
}
@Article{Hamming:1965:NLB,
author = "R. W. Hamming and W. L. Mammel",
title = "A Note on the Location of the Binary Point in a
Computing Machine",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "260--261",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.264258",
ISSN = "0367-7508",
ISSN-L = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "The authors consider the low-level multiplication
circuit efficiency of placing the binary point before
or after the first bit. If the leading bit is equally
likely to be a 0 or a 1, then their analysis shows that
it is better to place the point before the leading bit.
However, they report that a more likely distribution is
logarithmic (as predicted by Benford's Law, although
the Newcomb / Benford work is neither mentioned nor
cited), in which case there is no advantage for either
choice of placement of the binary point. They conclude
that it would be humane to place it after the leading
digit, by analogy with how people learn decimal
arithmetic.",
}
@Article{Konheim:1965:MDT,
author = "Alan G. Konheim",
title = "Mantissa Distributions (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "143--144",
month = apr,
year = "1965",
CODEN = "MCMPAF",
DOI = "http://dx.doi.org/10.2307/2004111",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Zipf:1965:PBL,
author = "George Kingsley Zipf",
title = "The psycho-biology of language: an introduction to
dynamic philology",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "xv + 336",
year = "1965",
LCCN = "P105 .Z5 1965",
bibdate = "Wed Nov 16 09:07:09 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
prodorbis.library.yale.edu:7090/voyager",
acknowledgement = ack-nhfb,
author-dates = "1902--1950",
remark = "Reprint of \cite{Zipf:1935:PBL}.",
subject = "language; philology; semantics; psycholinguistics;
comparative linguistics",
}
@Article{Ball:1966:BRB,
author = "R. J. Ball",
title = "Book Review: {{\booktitle{Random Processes and the
Growth of Firms: A Study of the Pareto Law}}, by Josef
Steindl}",
journal = j-J-R-STAT-SOC-SER-A-GENERAL,
volume = "129",
number = "4",
pages = "600--601",
month = "????",
year = "1966",
CODEN = "JSSAEF",
DOI = "http://dx.doi.org/10.2307/2982275",
ISSN = "0035-9238",
bibdate = "Sat Jan 24 11:18:12 MST 2015",
bibsource = "http://www.jstor.org/stable/i349635;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-a-1960.bib",
URL = "http://www.jstor.org/stable/2982275",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series A
(General)",
journal-URL = "http://www.jstor.org/journals/00359238.html",
}
@Book{Feller:1966:IPT,
author = "William Feller",
title = "Introduction to Probability Theory",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Second",
pages = "xviii + 626",
year = "1966",
ISSN = "0271-6232",
LCCN = "QA273 .F3727 1966",
bibdate = "Mon Nov 14 09:57:35 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Wiley series in probability and mathematical
statistics. Probability and mathematical statistics",
acknowledgement = ack-nhfb,
author-dates = "William Feller (1906--1970)",
remark = "Benford's Law is discussed on p. 62.",
}
@Article{Flehinger:1966:PRI,
author = "B. J. (Betty J.) Flehinger",
title = "On the probability that a random integer has initial
digit {$A$}",
journal = j-AMER-MATH-MONTHLY,
volume = "73",
number = "10",
pages = "1056--1061",
month = dec,
year = "1966",
CODEN = "AMMYAE",
DOI = "http://dx.doi.org/10.2307/2314636",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Sat Nov 12 15:33:14 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2314636",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Book{Petersen:1966:RMT,
author = "Gordon Marshall Petersen",
title = "Regular Matrix Transformations",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "viii + 142",
year = "1966",
LCCN = "QA263 .P415 1966",
bibdate = "Mon Nov 14 10:18:15 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Duncan:1967:AUD,
author = "R. L. Duncan",
title = "An Application of Uniform Distributions to the
{Fibonacci} Numbers",
journal = j-FIB-QUART,
volume = "5",
number = "2",
pages = "137--140",
month = apr,
year = "1967",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:04:52 MDT 2011",
bibsource = "http://www.fq.math.ca/5-2.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/5-2/duncan.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Mosteller:1967:DSR,
author = "Frederick Mosteller and Cleo Youtz and Douglas Zahn",
title = "The Distribution of Sums of Rounded Percentages",
journal = j-DEMOGRAPHY,
volume = "4",
number = "2",
pages = "850--858",
month = jun,
year = "1967",
CODEN = "????",
ISSN = "0070-3370 (print), 1533-7790 (electronic)",
ISSN-L = "0070-3370",
bibdate = "Thu Nov 24 08:03:16 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
note = "See \cite{Diaconis:1979:RP} for further work.",
URL = "http://muse.jhu.edu/journals/dem/;
http://www.biomedsearch.com/nih/Distribution-Sums-Rounded-Percentages/21318695.html;
http://www.jstor.org/stable/2060324",
abstract = "When percentages are computed for counts in several
categories or for several positive measurements0 each
taken as a fraction of their sum, the rounded
percentages often fail to add to 100 percent. We
investigate how frequently this failure occurs and what
the distributions of sums of rounded percentages are
for (1) an empirical set of data, (2) the multinomial
distribution in small samples, (3) spacings between
points dropped on an interval --- the broken-stick
model; and (4) for simulation for several categories.
The several methods produce similar distributions.We
find that the probability that the sum of rounded
percentages adds to exactly 100 percent is certain for
two categories, about three-fourths for three
categories, about two-thirds for four categories, and
about [Formula: see text] for larger numbers of
categories, c, on the average when categories are not
improbable.",
acknowledgement = ack-nhfb,
fjournal = "Demography",
pubmedid = "21318695",
}
@Article{Adhikari:1968:DMS,
author = "A. K. Adhikari and B. P. Sarkar",
title = "Distribution of most significant digit in certain
functions whose arguments are random variables",
journal = j-SANKHYA-B,
volume = "30",
number = "??",
pages = "47--58",
month = "????",
year = "1968",
CODEN = "SANBBV",
ISSN = "0581-5738",
ISSN-L = "0581-5738",
bibdate = "Sat Nov 12 16:09:30 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Sankhya Ser. B (Indian J. of Statist.)",
fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B.
Methodological",
}
@Book{Feller:1968:IPT,
author = "William Feller",
title = "Introduction to Probability Theory and its
Applications",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Third",
pages = "xviii + 509",
year = "1968",
ISBN = "0-471-25708-7",
ISBN-13 = "978-0-471-25708-0",
LCCN = "QA273 .F3713",
bibdate = "Mon Nov 14 09:57:35 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Berger:2010:FFFa,Berger:2010:FFFb} for a
discussion of flaws in the derivation of Benford's Law
in this book.",
acknowledgement = ack-nhfb,
author-dates = "William Feller (1906--1970)",
remark = "Pages 63--64 (of xxiv + 669) in 1971 printing have
only brief mention of two papers
\cite{Benford:1938:LAN,Pinkham:1961:DFS}.",
}
@Article{Shenton:1968:PDM,
author = "L. R. Shenton",
title = "Periodicity and Density of Modified {Fibonacci}
Sequences",
journal = j-FIB-QUART,
volume = "6",
number = "2",
pages = "109--116",
month = apr,
year = "1968",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:02 MDT 2011",
bibsource = "http://www.fq.math.ca/6-2.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/6-2/shenton.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
keywords = "Benford's Law",
}
@Article{Wilk:1968:PPM,
author = "M. B. Wilk and R. Gnanadesikan",
title = "Probability Plotting Methods for the Analysis of
Data",
journal = j-BIOMETRIKA,
volume = "55",
number = "1",
pages = "1--17",
month = mar,
year = "1968",
CODEN = "BIOKAX",
DOI = "http://dx.doi.org/10.2307/2334448",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
bibdate = "Sat Jun 21 14:33:29 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315458;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/biometrika1960.bib",
URL = "http://www.jstor.org/stable/2334448",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://www.jstor.org/journals/00063444.html",
keywords = "empirical cumulative distribution function (ECDF);
percent ($p$--$p$) plots; quantile ($q$--$q$) plots",
remark = "This article does not mention Benford's Law, but MJN
\cite{Nigrini:2012:BLA} lists this reference for
analysis of data.",
}
@Article{Adhikari:1969:SRD,
author = "A. K. Adhikari",
title = "Some results on the distribution of the most
significant digit",
journal = j-SANKHYA-B,
volume = "31",
number = "??",
pages = "413--420",
month = "????",
year = "1969",
CODEN = "SANBBV",
ISSN = "0581-5738",
ISSN-L = "0581-5738",
bibdate = "Sat Nov 12 16:12:50 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Sankhya Ser. B (Indian J. of Statist.)",
fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B.
Methodological",
}
@Article{Bumby:1969:FAM,
author = "R. Bumby and E. Ellentuck",
title = "Finitely additive measures and the first digit
problem",
journal = j-FUNDAM-MATH,
volume = "65",
number = "??",
pages = "33--42",
month = "????",
year = "1969",
CODEN = "????",
ISSN = "0016-2736",
ISSN-L = "0016-2736",
bibdate = "Sat Nov 12 16:19:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Fundamenta mathematicae",
}
@Article{Duncan:1969:NID,
author = "R. L. Duncan",
title = "Note on the Initial Digit Problem",
journal = j-FIB-QUART,
volume = "7",
number = "5",
pages = "474--475",
month = dec,
year = "1969",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:21 MDT 2011",
bibsource = "http://www.fq.math.ca/7-5.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/7-5/duncan.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Fairthorne:1969:PDE,
author = "Robert A. Fairthorne",
title = "Progress in Documentation: Empirical Hyperbolic
Distributions ({Bradford--Zipf--Mandelbrot}) for
Bibliometric Description and Prediction",
journal = j-J-DOC,
volume = "25",
number = "4",
pages = "313--343",
month = dec,
year = "1969",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/eb026481",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 06:27:27 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Reprinted in \cite{Fairthorne:2005:PDE}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
remark = "According to \cite{Potter:1981:LLR}, this paper is the
first to link the distributions of Bradford, Zipf,
Mandelbrot, and Lotka.",
}
@Unpublished{Hafner:1969:CSR,
author = "Everett M. Hafner",
title = "Circular slide roulette",
year = "1969",
bibdate = "Mon Nov 14 10:00:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Unpublished but dated 1969. Presented in 1975 in an
address at Hampshire College, Amherst, MA, USA",
acknowledgement = ack-nhfb,
}
@Article{Haight:1969:TPD,
author = "F. A. Haight",
title = "Two probability distributions connected with {Zipf}'s
rank-size conjecture",
journal = j-ZASTOS-MAT,
volume = "10",
pages = "225--228",
year = "1969",
CODEN = "ZAMTAK",
ISSN = "0044-1899",
ISSN-L = "0044-1899",
MRclass = "62.31",
MRnumber = "0246425 (39 \#7729)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Polska Akademia Nauk. Instytut Matematyczny.
Zastosowania Matematyki",
}
@Book{Knuth:1969:SNM,
author = "Donald E. Knuth",
title = "Semi\-nu\-mer\-i\-cal Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xi + 624",
year = "1969",
ISBN = "0-201-03802-1",
ISBN-13 = "978-0-201-03802-6",
LCCN = "QA76.5 .K57",
bibdate = "Wed Dec 15 15:47:38 1993",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Benford's Law is discussed on pp. 219--229.",
price = "US\$19.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
}
@Article{Kuipers:1969:RPR,
author = "L. Kuipers",
title = "Remark on a Paper by {R. L. Duncan} Concerning the
Uniform Distribution Mod $1$ of the Sequence of the
Logarithms of the {Fibonacci} Numbers",
journal = j-FIB-QUART,
volume = "7",
number = "5",
pages = "465--466",
month = dec,
year = "1969",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:21 MDT 2011",
bibsource = "http://www.fq.math.ca/7-5.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/7-5/kuipers-a.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Raimi:1969:DFS,
author = "R. A. Raimi",
title = "On the Distribution of First Significant Figures",
journal = j-AMER-MATH-MONTHLY,
volume = "76",
number = "4",
pages = "342--348",
month = apr,
year = "1969",
CODEN = "AMMYAE",
DOI = "http://dx.doi.org/10.2307/2316424",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:39:22 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Article{Raimi:1969:PDF,
author = "R. Raimi",
title = "The peculiar distribution of first significant
digits",
journal = j-SCI-AMER,
volume = "221",
number = "6",
pages = "109--120",
month = dec,
year = "1969",
CODEN = "SCAMAC",
DOI = "http://dx.doi.org/10.1038/scientificamerican1269-109",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Sat Nov 12 16:39:08 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@PhdThesis{Wong:1969:GDS,
author = "James Teng Wong",
title = "On the Generalization of the Distribution of the
Significant Digits Under Computation",
type = "{Ph.D.} thesis",
school = "Department of Mathematics, Oregon State University",
address = "Corvallis, OR, USA",
pages = "52",
year = "1969",
bibdate = "Fri Nov 25 15:41:42 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://search.proquest.com/docview/302476508?accountid=14677",
acknowledgement = ack-nhfb,
}
@Article{Aigner:1970:EPL,
author = "Dennis J. Aigner and Arthur S. Goldberger",
title = "Estimation of {Pareto's Law} from Grouped
Observations",
journal = j-J-AM-STAT-ASSOC,
volume = "65",
number = "330",
pages = "712--723",
month = jun,
year = "1970",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:44 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314212;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
URL = "http://www.jstor.org/stable/2284582",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Blum:1970:SID,
author = "M. Blum",
title = "On the Sums of Independently Distributed {Pareto}
Variates",
journal = j-SIAM-J-APPL-MATH,
volume = "19",
number = "1",
pages = "191--198",
month = jul,
year = "1970",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
}
@Article{Brown:1970:MOU,
author = "J. L. {Brown, Jr.} and R. L. Duncan",
title = "Modulo One Uniform Distribution of the Sequence of
Logarithms of Certain Recursive Sequences",
journal = j-FIB-QUART,
volume = "8",
number = "5",
pages = "482--486",
month = dec,
year = "1970",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:31 MDT 2011",
bibsource = "http://www.fq.math.ca/8-5.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
note = "See remark \cite{Kuipers:1973:RPD}.",
URL = "http://www.fq.math.ca/Scanned/8-5/brown.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Hamming:1970:DN,
author = "R. W. Hamming",
title = "On the Distribution of Numbers",
journal = j-BELL-SYST-TECH-J,
volume = "49",
number = "8",
pages = "1609--1625",
month = oct,
year = "1970",
CODEN = "BSTJAN",
ISSN = "0005-8580",
ISSN-L = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html;
http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf;
http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf",
abstract = "This paper examines the distribution of the mantissas
of floating-point numbers and shows how the arithmetic
operations of a computer transform various
distributions toward the limiting distribution $$ r(x)
= 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where
$b$ is the base of the number system). The paper also
gives a number of applications to hardware, software,
and general computing which show that this distribution
is not merely an amusing curiosity. A brief examination
of the distribution of exponents is include.",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Hill:1970:ZLP,
author = "Bruce M. Hill",
title = "{Zipf}'s law and prior distributions for the
composition of a population",
journal = j-J-AM-STAT-ASSOC,
volume = "65",
number = "331",
pages = "1220--1232",
month = sep,
year = "1970",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62.35",
MRnumber = "0279936 (43 \#5657)",
MRreviewer = "I. J. Good",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
URL = "http://www.jstor.org/stable/2284288",
ZMnumber = "Zbl 0224.92011",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Orlov:1970:GZM,
author = "Ju. K. Orlov",
title = "A generalization of the {Zipf--Mandelbrot} law",
journal = "Sakharthvelos SSR Mecnierebatha Akademiis Moambe",
volume = "57",
pages = "37--40",
year = "1970",
CODEN = "????",
ISSN = "????",
MRclass = "94.50",
MRnumber = "0274234 (42 \#9109)",
MRreviewer = "T. Nemetz",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Sakharth. SSR Mech. Akad. Moambe",
}
@Article{Taguchi:1970:ZLC,
author = "Tokio Taguchi",
title = "On {Zipf}'s law. {A} characterization of distributions
in linguistics and demography",
journal = j-PROC-INST-STATIST-MATH,
volume = "17",
pages = "83--90",
year = "1970",
CODEN = "????",
ISSN = "0912-6112",
ISSN-L = "0912-6112",
bibdate = "Sat Nov 12 10:39:57 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0238.68026",
acknowledgement = ack-nhfb,
ajournal = "Proc. Inst. Statist. Math.",
classmath = "68Q45 (Formal languages)",
fjournal = "Proceedings of the Institute of Statistical
Mathematics",
language = "Japanese",
}
@Book{Zeller:1970:TLG,
author = "Karl Zeller and Wolfgang Beekmann",
title = "{Theorie der Limitierungsverfahren}. (German)
[{Theory} of limiting processes]",
volume = "15",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xii + 314",
year = "1970",
LCCN = "QA295 .Z4 1970",
bibdate = "Wed Nov 16 06:43:43 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Ergebnisse der Mathematik und ihrer Grenzgebiete",
acknowledgement = ack-nhfb,
language = "German",
subject = "series; convergence",
}
@Article{Thorp:1971:PCD,
author = "E. Thorp and R. Whitley",
title = "{Poincar{\'e}}'s conjecture and the distribution of
digits in logarithm tables",
journal = j-COMPOS-MATH,
volume = "21",
number = "??",
pages = "233--250",
month = "????",
year = "1971",
CODEN = "CMPMAF",
ISSN = "0010-437X (print), 1570-5846 (electronic)",
ISSN-L = "0010-437X",
bibdate = "Sat Nov 12 16:36:41 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Comp. Math.",
fjournal = "Compositio Mathematica",
}
@Article{Wlodarski:1971:FLN,
author = "J. Wlodarski",
title = "{Fibonacci} and {Lucas} Numbers Tend to Obey
{Benford's Law}",
journal = j-FIB-QUART,
volume = "9",
number = "1",
pages = "87--88",
month = feb,
year = "1971",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:33 MDT 2011",
bibsource = "http://www.fq.math.ca/9-1.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/9-1/wlodarski2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Aigner:1972:CEP,
author = "Dennis J. Aigner and Arthur S. Goldberger",
title = "Corrigenda: Estimation of {Pareto's Law} from Grouped
Observations",
journal = j-J-AM-STAT-ASSOC,
volume = "67",
number = "337",
pages = "252--252",
month = mar,
year = "1972",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:45 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314217;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
URL = "http://www.jstor.org/stable/2284755",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Krevitt:1972:CSZ,
author = "Beth Krevitt and Belver C. Griffith",
title = "A comparison of several {Zipf}-type distributions in
their goodness of fit to language data",
journal = j-J-AM-SOC-INF-SCI,
volume = "23",
number = "3",
pages = "220--221",
year = "1972",
CODEN = "AISJB6",
DOI = "http://dx.doi.org/10.1002/asi.4630230310",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
}
@Article{Varian:1972:LEB,
author = "Hal R. Varian",
title = "Letter to the {Editor}: {Benford's Law}",
journal = j-AMER-STAT,
volume = "26",
number = "3",
pages = "65--66",
month = jun,
year = "1972",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Mar 30 11:34:37 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://links.jstor.org/sici?sici=0003-1305%28197206%2926%3A3%3C62%3ALTTE%3E2.0.CO%3B2-Q",
abstract = "Around 1938 the physicist Frank Benford observed a
rather strange fact: tables of logarithms in libraries
tend to be dirtier at the beginning than at the end.
This indicated to Benford that people had more occasion
to calculate with numbers beginning with 1 or 2 than
with 8 or 9.\par
Benford also found that the frequency of the digit $p$
being the first digit of a decimal number was very
closely approximated by $ \log (p + 1) - \log p $
[i.e., $ \log (1 + 1 / p) $ ]. This has become known as
Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Vlachy:1972:VFS,
author = "Jan Vlach{\'y}",
title = "Variable Factors in Scientific Communities
(Observations on {Lotka's Law})",
journal = "Teorie a Metoda",
volume = "4",
number = "??",
pages = "91--120",
month = "????",
year = "1972",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Nov 25 07:53:43 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
xxvolume = "6",
}
@Article{Whitney:1972:MNI,
author = "R. E. Whitney",
title = "Mathematical Notes: Initial Digits for the Sequence of
Primes",
journal = j-AMER-MATH-MONTHLY,
volume = "79",
number = "2",
pages = "150--152",
month = feb,
year = "1972",
CODEN = "AMMYAE",
DOI = "http://dx.doi.org/10.2307/2316536",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:38 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Article{Wilkinson:1972:ABL,
author = "Elizabeth A. Wilkinson",
title = "The Ambiguity of {Bradford's Law}",
journal = j-J-DOC,
volume = "28",
number = "2",
pages = "122--130",
month = "????",
year = "1972",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/eb026534",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:20:34 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@TechReport{Diaconis:1973:LMI,
author = "Persi Diaconis",
title = "Limits of measures of the integers with applications
to random number generators and the distribution of
leading digits",
type = "Memorandum",
number = "NS-211",
institution = "Department of Statistics, Harvard University",
address = "Cambridge, MA, USA",
day = "22",
month = mar,
year = "1973",
bibdate = "Sat Nov 12 16:23:20 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Kreifelts:1973:OBG,
author = "Thomas Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine
Gleitkomma-Arithmetik}. ({German}) [{Optimal} Choice of
Basis for a Floating-Point Arithmetic]",
journal = j-COMPUTING,
volume = "11",
number = "4",
pages = "353--363",
month = dec,
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/computing.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
note = "See correction \cite{Kreifelts:1975:OBF}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Inst. Numerische Datenverarbeitung, Bonn, West
Germany",
classification = "723; 921; C5230",
description = "digital arithmetic",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput (Vienna/NY)",
keywords = "base; computer programming; floating point arithmetic;
mathematical techniques; optimal choice; rounding
errors",
language = "German",
}
@Article{Kuipers:1973:RPD,
author = "L. Kuipers and Jau-shyong Shiue",
title = "Remark on a Paper by {Duncan} and {Brown} on the
Sequence of Logarithms of Certain Recursive Sequences",
journal = j-FIB-QUART,
volume = "11",
number = "3",
pages = "292--293",
month = oct,
year = "1973",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:42 MDT 2011",
bibsource = "http://www.fq.math.ca/11-3.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
note = "See \cite{Brown:1970:MOU}.",
URL = "http://www.fq.math.ca/Scanned/11-3/kuipers.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Murphy:1973:LLH,
author = "Larry J. Murphy",
title = "{Lotka's Law} in the Humanities?",
journal = j-J-AM-SOC-INF-SCI,
volume = "24",
number = "6",
pages = "461--462",
month = nov # "\slash " # dec,
year = "1973",
CODEN = "AISJB6",
DOI = "http://dx.doi.org/10.1002/asi.4630240607",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Nov 25 08:09:40 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
}
@Article{Petruszewycz:1973:LLE,
author = "M. Petruszewycz",
title = "{L'histoire} de la loi d'{Estoup--Zipf}: documents.
({French}) [{The} history of the {Estoup--Zipf} law]",
journal = "Math. Sci. Humaines",
volume = "??",
number = "44",
pages = "41--56",
year = "1973",
CODEN = "????",
ISSN = "0025-5815",
ISSN-L = "0025-5815",
MRclass = "92A25",
MRnumber = "0354071 (50 \#6553)",
MRreviewer = "J. S. Joel",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Centre de Math{\'e}matique Sociale. \'Ecole Pratique
des Hautes \'Etudes. Math{\'e}matiques et Sciences
Humaines",
language = "French",
}
@Article{Sarkar:1973:OSD,
author = "B. P. Sarkar",
title = "An observation on the significant digits of the
binomial coefficients and factorials",
journal = j-SANKHYA-B,
volume = "35",
number = "??",
pages = "363--364",
month = "????",
year = "1973",
CODEN = "SANBBV",
ISSN = "0581-5738",
ISSN-L = "0581-5738",
bibdate = "Sat Nov 12 16:29:39 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Sankhya Ser. B (Indian J. of Statist.)",
fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B.
Methodological",
}
@Article{Schatte:1973:VMG,
author = "Peter Schatte",
title = "{Zur Verteilung der Mantisse in der
Gleitkommadarstellung einer Zufallsgr{\"o}{\ss}e}.
({German}) [Distribution of the mantissa in the
floating-point representation of a random variable]",
journal = j-Z-ANGE-MATH-MECH,
volume = "53",
number = "??",
pages = "553--565",
month = "????",
year = "1973",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Mon Nov 14 16:35:28 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
language = "German",
}
@Article{Sentance:1973:FAB,
author = "W. A. Sentance",
title = "A Further Analysis of {Benford's Law}",
journal = j-FIB-QUART,
volume = "11",
number = "5",
pages = "490--494",
month = dec,
year = "1973",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:46 MDT 2011",
bibsource = "http://www.fq.math.ca/11-5.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/11-5/sentance.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Banks:1974:AMN,
author = "William P. Banks and David K. Hill",
title = "The apparent magnitude of number scaled by random
production",
journal = j-J-EXP-PSYCH-GEN,
volume = "102",
number = "2",
pages = "353--376",
month = feb,
year = "1974",
CODEN = "JPGEDD",
DOI = "http://psycnet.apa.org/doi/10.1037/h0035850",
ISSN = "0096-3445 (print), 1939-2222 (electronic)",
ISSN-L = "0096-3445",
bibdate = "Fri Feb 15 06:32:17 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://psycnet.apa.org/journals/xge/102/2/353/;
http://psycnet.apa.org/psycinfo/1974-24305-001",
acknowledgement = ack-nhfb,
fjournal = "Journal of Experimental Psychology: General",
}
@PhdThesis{Diaconis:1974:WSA,
author = "Persi Diaconis",
title = "Weak and Strong Averages in probability and the theory
numbers",
type = "{Ph.D.} thesis",
school = "Department of Statistics, Harvard University",
address = "Cambridge, MA, USA",
pages = "xvii + 117",
year = "1974",
bibdate = "Mon Nov 14 10:26:03 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Duran:1974:ACS,
author = "J. Peter Duran",
title = "Almost convergence, summability and ergodicity",
journal = j-CAN-J-MATH,
volume = "26",
number = "??",
pages = "372--387",
month = "????",
year = "1974",
CODEN = "CJMAAB",
DOI = "http://dx.doi.org/10.4153/CJM-1974-039-6",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
bibdate = "Sat Sep 10 15:38:45 MDT 2011",
bibsource = "http://cms.math.ca/cjm/v26/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/canjmath1970.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics = Journal canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
remark = "In relation to Benford's Law, see theorem 6.2.",
}
@Article{Hill:1974:RFF,
author = "Bruce M. Hill",
title = "The rank-frequency form of {Zipf}'s law",
journal = j-J-AM-STAT-ASSOC,
volume = "69",
number = "348",
pages = "1017--1026",
month = dec,
year = "1974",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62E15",
MRnumber = "0426242 (54 \#14188)",
MRreviewer = "S. M. Samuels",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
ZMnumber = "Zbl 0301.60011",
acknowledgement = ack-nhfb,
classification = "B0240 (Probability and statistics); C1140
(Probability and statistics)",
corpsource = "Dept. of Statistics, Univ. of Michigan, Ann Arbor, MI,
USA",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "Bose--Einstein allocation; distribution; random
processes; rank frequency form; statistics; Zipf's
law",
treatment = "T Theoretical or Mathematical",
}
@Book{Kuipers:1974:UDS,
author = "Lauwerens Kuipers and Harald Niederreiter",
title = "Uniform distribution of sequences",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiv + 390",
year = "1974",
ISBN = "0-471-51045-9",
ISBN-13 = "978-0-471-51045-1",
LCCN = "QA292 .K84",
bibdate = "Sat Nov 12 15:42:53 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "``A Wiley-Interscience publication.''.",
subject = "Sequences (Mathematics); Uniform distribution
(Probability theory)",
}
@Article{Schorr:1974:LLL,
author = "Alan E. Schorr",
title = "{Lotka's Law} and Library Science",
journal = "RQ",
volume = "14",
number = "1",
pages = "32--33",
month = "Fall",
year = "1974",
CODEN = "????",
ISSN = "0033-7072",
ISSN-L = "0033-7072",
bibdate = "Fri Nov 25 08:12:46 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "RQ",
fjournal = "Reference Quarterly",
}
@Unpublished{Singmaster:1974:RSB,
author = "D. Singmaster",
title = "Recurrent sequences and {Benford}'s law",
year = "1974",
bibdate = "Sat Nov 12 16:25:29 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Preprint submitted to Fibonacci Quarterly in 1974, but
never published there.",
acknowledgement = ack-nhfb,
}
@Book{Sterbenz:1974:FPC,
author = "Pat H. Sterbenz",
title = "Floating Point Computation",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiv + 316",
year = "1974",
ISBN = "0-13-322495-3",
ISBN-13 = "978-0-13-322495-5",
LCCN = "QA76.8.I12 S771 1974",
MRclass = "68A05 (65G05)",
MRnumber = "50 1556",
bibdate = "Sat May 29 08:01:36 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Prentice-Hall Series in Automatic Computation.",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "Compiling (Electronic computers); Computation by
computer systems --- Floating point representation;
Floating-point arithmetic; IBM 360 (Computer) ---
Programming",
remark = "From p. 116: ``There is general agreement that the
mantissas of floating-point numbers are not uniformly
distributed. [See Hamming (1962)
[\cite{Hamming:1962:NMS}], Pinkham (1961)
[Pinkham:1961:DFS], or Knuth (1969) [Knuth:1969:SNM].]
Instead, it is customary to assume that they are
distributed logarithmically, that is, that the
probability density function is
$$ (3.12.9) f(m) = \frac {1}{m \ln r}, \qquad r^{-1}
\leq m \leq 1. $$
This assumption is based on the following observations:
First, this distribution reproduces itself under
multiplication, but a uniform distribution does not.
[See Hamming (1962) [\cite{Hamming:1962:NMS}] and
Exercise 20.] A second justification is based on the
fact that many of the numbers that arise in computation
represent measurable quantities such as lengths,
forces, etc., and it is reasonable to believe that the
distribution of the mantissas of such quantities is
independent of the units in which they are measured.
Pinkham (1961) shows that this leads to the conclusion
that the distribution of mantissas must be
logarithmic.''",
reviewer = "F. J. Murray",
}
@Article{Tsao:1974:DSD,
author = "Nai Kuan Tsao",
title = "On the Distributions of Significant Digits and
Roundoff Errors",
journal = j-CACM,
volume = "17",
number = "5",
pages = "269--271",
month = may,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65G05",
MRnumber = "49 6595",
MRreviewer = "N. N. Abdelmalek",
bibdate = "Mon Jan 22 07:26:38 MST 2001",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Tsao74;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Generalized logarithmic law is derived for the
distribution of the first $t$ significant digits of a
random digital integer. This result is then used to
determine the distribution of the roundoff errors in
floating-point operations, which is a mixture of
uniform and reciprocal distributions.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "921",
corpsource = "Aerospace Res. Labs., Wright-Patterson AFB, OH, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
journalabr = "Commun ACM",
keywords = "Benford's Law; digital arithmetic; digital integer;
distributions; error analysis; floating point
operations; Law of Anomalous Numbers; logarithmic law;
mathematical techniques; mean value; random;
reciprocal; roundoff errors; significant digits;
uniform distribution; variance; Zipf's Law",
oldlabel = "Tsao74",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Tsao74",
}
@Article{Voos:1974:LIS,
author = "Henry Voos",
title = "{Lotka} and Information Science",
journal = j-J-AM-SOC-INF-SCI,
volume = "25",
number = "4",
pages = "270--272",
month = jul # "\slash " # aug,
year = "1974",
CODEN = "AISJB6",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Nov 25 08:14:01 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
keywords = "Lotka's Law",
}
@Article{Yavuz:1974:ZLE,
author = "Davras Yavuz",
title = "{Zipf}'s law and entropy",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "20",
number = "5",
pages = "650--650",
year = "1974",
CODEN = "IETTAW",
DOI = "http://dx.doi.org/10.1109/TIT.1974.1055269",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Sat Nov 12 10:43:30 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0295.94048",
acknowledgement = ack-nhfb,
classmath = "94A15 (General topics of information theory)",
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}
@InProceedings{Bennett:1975:SDI,
author = "John M. Bennett",
booktitle = "Int. Comput. Symp. 1975, Proc., Antibes, (1975)",
title = "Storage design for information retrieval: {Scarrott}'s
conjecture and {Zipf}'s law",
publisher = "????",
address = "????",
pages = "233--237",
year = "1975",
bibdate = "Sat Nov 12 10:49:15 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0322.68068",
acknowledgement = ack-nhfb,
classmath = "68P20 (Information storage and retrieval) 68N01
(General)",
}
@Book{Hardy:1975:ITN,
author = "Godfrey H. Hardy and Edward M. Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
edition = "Fourth",
pages = "421",
year = "1975",
ISBN = "0-19-853310-1",
ISBN-13 = "978-0-19-853310-8",
LCCN = "????",
bibdate = "Fri Jun 24 12:32:14 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Hill:1975:SFZ,
author = "Bruce M. Hill and Michael Woodroofe",
title = "Stronger forms of {Zipf}'s law",
journal = j-J-AM-STAT-ASSOC,
volume = "70",
number = "349",
pages = "212--219",
month = mar,
year = "1975",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62E15 (62D05)",
MRnumber = "0440763 (55 \#13633)",
MRreviewer = "I. J. Good",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
ZMnumber = "Zbl 0326.92014",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Kemperman:1975:BDM,
author = "J. H. B. Kemperman",
title = "Bounds on the discrepancy modulo $1$ of a real random
variable",
journal = j-BULL-INST-MATH-STAT,
volume = "4",
number = "??",
pages = "138--??",
month = "????",
year = "1975",
CODEN = "SMBCVA",
ISSN = "0146-3942",
ISSN-L = "0146-3942",
bibdate = "Sat Nov 12 16:26:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Abstract no. 75t-47.",
acknowledgement = ack-nhfb,
fjournal = "Bulletin --- Institute of Mathematical Statistics",
}
@Article{Kreifelts:1975:OBF,
author = "T. Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik
(Berichtigung)} ({German}) {Optimal Basis Choice for a
Floating-Point Arithmetic (Correction)}",
journal = j-COMPUTING,
volume = "14",
number = "3",
pages = "313--314",
month = sep,
year = "1975",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/computing.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Kreifelts:1973:OBG}.",
acknowledgement = ack-nj,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{Partridge:1975:DDW,
author = "D. Partridge",
title = "A dynamic database which automatically removes
unwanted generalisation for the efficient analysis of
language features that exhibit a disparate frequency
distribution",
journal = j-COMP-J,
volume = "18",
number = "1",
pages = "43--48",
month = feb,
year = "1975",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/43.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/44.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/45.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/46.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/47.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/48.tif",
abstract = "A self-organising database was developed as part of a
general language analysis system. The periodic,
automatic reorganisation of the database was aimed at
increasing the efficiency of analysis of a language in
which the constituent features exhibit a Zipfian type
rank-frequency relationship. Such a distribution means
that only a small number of features account for a
large proportion of the information, while a large
number of possible features are seldom encountered and
thus seldom accessed within the database. The mechanism
described aims at reconciling two conflicting
procedures: condensation by generalisation of language
features to minimise the total size of the database,
and the particularisation of the few commonly occurring
features to minimise the average analysis time. Results
are presented for the application of this mechanism to
the analysis of batches of FORTRAN programs that
constituted part of the `normal' workload for computers
within five different environments.",
acknowledgement = ack-nhfb,
classcodes = "C6120 (File organisation); C7820 (Humanities
computing)",
classification = "723",
corpsource = "Univ. Nairobi, Kenya",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "analysis; data bases; data processing; disparate
frequency distribution; dynamic database; file
organisation; language; language translation and
linguistics; self organising; unwanted generalisation",
treatment = "P Practical",
}
@Article{Schorr:1975:LLH,
author = "Alan E. Schorr",
title = "{Lotka's Law} and the History of Legal Medicine",
journal = "Research in Librarianship",
volume = "30",
number = "??",
pages = "205--209",
month = sep,
year = "1975",
CODEN = "????",
ISSN = "0034-5245",
ISSN-L = "0034-5245",
bibdate = "Fri Nov 25 08:17:00 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Res. Librarianship",
}
@Article{Schorr:1975:LLM,
author = "Alan E. Schorr",
title = "{Lotka's Law} and Map Librarianship",
journal = j-J-AM-SOC-INF-SCI,
volume = "26",
number = "3",
pages = "189--190",
month = may # "\slash " # jun,
year = "1975",
CODEN = "AISJB6",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Nov 25 08:11:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
}
@Article{Webb:1975:DFD,
author = "William Webb",
title = "Distribution of the First Digits of {Fibonacci}
Numbers",
journal = j-FIB-QUART,
volume = "13",
number = "4",
pages = "334--336",
month = dec,
year = "1975",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:03 MDT 2011",
bibsource = "http://www.fq.math.ca/13-4.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/13-4/webb.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
keywords = "Benford's Law",
}
@Article{Woodroofe:1975:ZL,
author = "Michael Woodroofe and Bruce Hill",
title = "On {Zipf}'s law",
journal = j-J-APPL-PROBAB,
volume = "12",
number = "3",
pages = "425--434",
month = sep,
year = "1975",
CODEN = "JPRBAM",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
MRclass = "62E20 (62P10)",
MRnumber = "0440764 (55 \#13634)",
MRreviewer = "I. J. Good",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/3212857",
ZMnumber = "Zbl 0343.60012",
abstract = "A Zipf's law is a probability distribution on the
positive integers which decays algebraically. Such laws
describe (approximately) a large class of phenomena. We
formulate a model for such phenomena and, in terms of
our model, give necessary and sufficient conditions for
a Zipf's law to hold.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Probability",
journal-URL = "http://www.jstor.org/journals/00219002.html;
http://projecteuclid.org/euclid.jap/",
keywords = "classical occupancy problem; laws of large numbers:
weak convergence; regularly varying functions",
}
@Article{Worthen:1975:ABL,
author = "Dennis B. Worthen",
title = "The Application of {Bradford's Law} to Monographs",
journal = j-J-DOC,
volume = "31",
number = "1",
pages = "19--25",
month = "????",
year = "1975",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/eb026590",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:18:55 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@Article{Billera:1976:PSC,
author = "Louis J. Billera and Robert E. Bixby",
title = "{Pareto} Surfaces of Complexity $1$",
journal = j-SIAM-J-APPL-MATH,
volume = "30",
number = "1",
pages = "81--89",
month = jan,
year = "1976",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classification = "B0250 (Combinatorial mathematics); C1160
(Combinatorial mathematics)",
corpsource = "Dept. of Math., Cornell Univ., Ithaca, NY, USA",
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
keywords = "1-commodity representation; attainable sets;
complexity 1; game theory; graph theory; Pareto
surfaces; set theory",
treatment = "T Theoretical or Mathematical",
}
@Article{Brambilla:1976:DDA,
author = "Francisco Brambilla",
title = "La distribuzione delle aziende secondo le dimensioni.
{Verifica} empirica della legge logonormale e di quella
di {Zipf} e nuovi modelli interpretativi. ({Italian})
[{The} distribution of firms by size. {Empirical} test
of the log-normal law and {Zipf}'s law and new models
of interpretation]",
journal = "Giornale degli Economisti e Annali de Economia (Nuova
Serie)",
volume = "35",
number = "3--4",
pages = "131--153, 235",
month = mar # "\slash " # apr,
year = "1976",
CODEN = "????",
ISSN = "0017-0097",
ISSN-L = "0017-0097",
MRclass = "90A15",
MRnumber = "0452510 (56 \#10789)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/23242834",
acknowledgement = ack-nhfb,
ajournal = "Giorn. Econom. Ann. Econom. (N.S.)",
fjournal = "Giornale degli Economisti e Annali de Economia",
language = "Italian",
}
@Article{Cohen:1976:EFD,
author = "Daniel I. A. Cohen",
title = "An explanation of the first digit phenomenon",
journal = j-J-COMB-THEORY-A,
volume = "20",
number = "3",
pages = "367--370",
month = may,
year = "1976",
CODEN = "JCBTA7",
ISSN = "0097-3165",
ISSN-L = "0097-3165",
bibdate = "Thu Feb 15 16:29:51 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Theory (Series A)",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Davis:1976:SRI,
author = "Basil Davis",
title = "Some Remarks on Initial Digits",
journal = j-FIB-QUART,
volume = "14",
number = "1",
pages = "13--14",
month = feb,
year = "1976",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:05 MDT 2011",
bibsource = "http://www.fq.math.ca/14-1.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/14-1/davis.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Feldstein:1976:CED,
author = "Alan Feldstein and Richard Goodman",
title = "Convergence Estimates for the Distribution of Trailing
Digits",
journal = j-J-ACM,
volume = "23",
number = "2",
pages = "287--297",
month = apr,
year = "1976",
CODEN = "JACOAH",
DOI = "http://doi.acm.org/10.1145/321941.321948",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "An analysis is made of the distribution of trailing
digits (tail end digits) of positive real
floating-point numbers represented in arbitrary base $
\beta $ and randomly chosen from a logarithmic
distribution. The analysis shows that the $n$ th digit
for $ n \geq 2 $ is actually approximately uniformly
distributed. The approximation depends upon both $n$
and the base beta. It becomes better as $n$ increases,
and it is exact in the limit as $ n \rightarrow \infty
$. A table of this distribution is presented for
various $ \beta $ and $n$, along with a table of the
maximum digit by digit deviation $ \Delta $ of the
logarithmic distribution from the uniform distribution.
Various asymptotic results for $ \Delta $ are
included.",
acknowledgement = ack-nhfb,
classification = "723",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
journalabr = "J Assoc Comput Mach",
keywords = "Benford's Law; computer arithmetic; computer
programming; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Orlov:1976:CBP,
author = "Ju. K. Orlov",
title = "The connection between the {Pareto} distribution and
the generalized {Zipf--Mandelbrot} law",
journal = "Sakharthvelos SSR Mecnierebatha Akademiis Moambe",
volume = "83",
number = "1",
pages = "57--60",
year = "1976",
CODEN = "????",
ISSN = "????",
MRclass = "90A15",
MRnumber = "0434355 (55 \#7321)",
MRreviewer = "S. Krcevinac",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Sakharth. SSR Mech. Akad. Moambe",
}
@Article{Raimi:1976:FDP,
author = "Ralph A. Raimi",
title = "The first digit problem",
journal = j-AMER-MATH-MONTHLY,
volume = "83",
number = "7",
pages = "521--538",
month = aug # "\slash " # sep,
year = "1976",
CODEN = "AMMYAE",
DOI = "http://dx.doi.org/10.2307/2319349",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Sat Nov 12 15:49:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2319349",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
remark = "This article surveys the literature up to 1976,
reports defects in several earlier mathematical
`explanations' of Benford's Law, and gives a 52-entry
bibliography of prior work. All of those entries are
incorporated in this bibliography. It criticizes parts
of \cite{Goudsmit:1944:SFN} as `dead wrong' (and the
author reiterates that view in \cite{Raimi:1985:FDP}).
See also later work \cite{Logan:1978:FDP}. On page 529,
Raimi writes ``If the first digits of all the tables in
the universe obey some fixed distribution law,
Stigler's or Benford's or some other, that law must
surely be independent of the system of units chosen,
since God is not known to favor either the metric
system or the English system. In other words, a
universal first digit law, if it exists, must be
scale-invariant.''",
remark-2 = "This is so far the second earliest reference that I
have found to \cite{Newcomb:1881:NFU}; the earliest is
\cite{Boring:1920:LNL}, which has only brief mention of
the question of digit frequencies. Raimi comments on p.
522: ``This assertion, whatever it may mean, will be
called Benford's Law because it has been thought by
many writers to have originated with the General
Electric Company physicist Frank Benford [2]. Certainly
Benford popularized the problem, and he may well have
been unaware that the polymathic Simon Newcomb,
primarily an astronomer but also sometime editor of The
American Journal of Mathematics, had also formulated
the same law 57 years earlier [1]. There is ample
precedent for naming laws and theorems for persons
other than their discoverers, else half of analysis
would be named after Euler. Besides, even Newcomb
implied that the observation giving rise to the Benford
law was an old one in his day. One would hate to change
the name of the law now only to find later that another
change was called for.''",
}
@Article{Rouault:1976:PAE,
author = "Alain Rouault",
title = "Propri{\'e}t{\'e}s asymptotiques d'un
{$n$}-{\'e}chantillon d'une variable al{\'e}atoire
d{\'e}nombrable connues sous le nom de lois de {Zipf}.
({French}) [Asymptotic properties of an $n$-sample of a
denumerable random variable known under the name of
{Zipf}'s law]",
journal = j-C-R-ACAD-SCI-PARIS-SER-AB,
volume = "283",
number = "6",
pages = "Aiv, A379--A380",
year = "1976",
CODEN = "CHASAP",
ISSN = "0151-0509",
ISSN-L = "0151-0509",
MRclass = "62E20",
MRnumber = "0423644 (54 \#11619)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Comptes Rendus Hebdomadaires des S{\'e}ances de
l'Acad{\'e}mie des Sciences. S{\'e}ries A et B",
language = "French",
}
@Article{Rouault:1976:SML,
author = "Alain Rouault",
title = "Sources markoviennes et lois de {Zipf}. ({French})
[{Markovian} source and {Zipf} laws]",
journal = j-C-R-ACAD-SCI-PARIS-SER-AB,
volume = "283",
number = "10",
pages = "Aiii, A789--A790",
year = "1976",
CODEN = "CHASAP",
ISSN = "0151-0509",
ISSN-L = "0151-0509",
MRclass = "62E20",
MRnumber = "0423645 (54 \#11620)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Comptes Rendus Hebdomadaires des S{\'e}ances de
l'Acad{\'e}mie des Sciences. S{\'e}ries A et B",
language = "French",
}
@Article{Vlachy:1976:TFL,
author = "Jan Vlach{\'y}",
title = "Time Factor in {Lotka's Law}",
journal = "Probleme de Informare si Documentare",
volume = "10",
number = "2",
pages = "44--87",
month = "????",
year = "1976",
CODEN = "PIDCA6",
ISSN = "0032-924X",
ISSN-L = "0032-924X",
bibdate = "Fri Nov 25 07:56:00 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Prob. inf. \& doc.",
}
@Article{Brookes:1977:TBL,
author = "Bertram C. Brookes",
title = "Theory of the {Bradford Law}",
journal = j-J-DOC,
volume = "33",
number = "3",
pages = "180--209",
month = "????",
year = "1977",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/eb026641",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:16:18 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@Article{Clark:1977:ESL,
author = "Douglas W. Clark and C. Cordell Green",
title = "An Empirical Study of List Structure in {Lisp}",
journal = j-CACM,
volume = "20",
number = "2",
pages = "78--87",
month = feb,
year = "1977",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:31:28 MST 2001",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Compiler/garbage.collection.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm20.html#ClarkG77;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Static measurements of the list structure of five
large Lisp programs are reported and analyzed. These
measurements reveal substantial regularity, or
predictability, among pointers to atoms and especially
among pointers to lists. Pointers to atoms are found to
obey, roughly, Zipf's law, which governs word
frequencies in natural languages; pointers to lists
usually point to a location physically nearby in
memory. The use of such regularities in the
space-efficient representation of list structure is
discussed.",
acknowledgement = ack-nhfb,
classcodes = "C6130 (Data handling techniques); C6140D (High level
languages)",
classification = "723",
comment = "Great paper; evidence pro CDR-coding, con fancy CONS",
corpsource = "Carnegie-Mellon Univ., Pittsburgh, PA, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
journalabr = "Commun ACM",
keywords = "computer programming languages; data processing ---
Data Structures; empirical study; LISP; list structure;
measurements; regularity",
oldlabel = "ClarkG77",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ClarkG77",
}
@Article{Coile:1977:LFD,
author = "Russell C. Coile",
title = "{Lotka}'s Frequency Distribution of Scientific
Productivity",
journal = j-J-AM-SOC-INF-SCI,
volume = "28",
number = "6",
pages = "366--370",
month = nov,
year = "1977",
CODEN = "AISJB6",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Nov 25 08:08:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
keywords = "Lotka's Law",
}
@Article{Diaconis:1977:DLD,
author = "Persi Diaconis",
title = "The distribution of leading digits and uniform
distribution $ \bmod 1 $",
journal = j-ANN-PROBAB,
volume = "5",
number = "1",
pages = "72--81",
month = feb,
year = "1977",
CODEN = "APBYAE",
DOI = "http://dx.doi.org/10.1214/aop/1176995891",
ISSN = "0091-1798",
ISSN-L = "0091-1798",
bibdate = "Sun Apr 20 10:44:17 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/annprobab1970.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/euclid.aop/1176995891",
acknowledgement = ack-nhfb,
fjournal = "Annals of Probability",
journal-URL = "http://projecteuclid.org/all/euclid.aop",
keywords = "Benford's Law",
}
@Article{Goudsmit:1977:PEP,
author = "Samuel Goudsmit",
title = "Pitfalls in Elementary Probability",
journal = j-PROC-AMER-PHIL-SOC,
volume = "121",
number = "2",
pages = "188--189",
day = "29",
month = apr,
year = "1977",
CODEN = "PAPCAA",
ISSN = "0003-049X",
bibdate = "Fri Mar 22 08:50:02 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Based on a lecture presented November 11, 1976.",
URL = "http://www.jstor.org/stable/986527",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
keywords = "Benford's Law; biased coin flips; biased dice throws;
roulette wheels",
}
@Article{Ylvisaker:1977:TR,
author = "Donald Ylvisaker",
title = "Test Resistance",
journal = j-J-AM-STAT-ASSOC,
volume = "72",
number = "359",
pages = "551--556",
month = sep,
year = "1977",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:48 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314242;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
URL = "http://www.jstor.org/stable/2286216",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Brady:1978:MBL,
author = "W. G. Brady",
title = "More on {Benford}'s Law",
journal = j-FIB-QUART,
volume = "16",
number = "1",
pages = "51--52",
month = feb,
year = "1978",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:24 MDT 2011",
bibsource = "http://www.fq.math.ca/16-1.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/16-1/brady.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Brookes:1978:FRD,
author = "Bertram C. Brookes and Jos{\'e} M. Griffiths",
title = "Frequency-rank distributions",
journal = j-J-AM-SOC-INF-SCI,
volume = "29",
number = "1",
pages = "5--13",
month = jan,
year = "1978",
CODEN = "AISJB6",
DOI = "http://dx.doi.org/10.1002/asi.4630290104",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Mon Feb 25 10:40:13 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1002/asi.4630290104/abstract",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
keywords = "Anomalous Law of Numbers; Benford's Law",
}
@PhdThesis{Chen:1978:ZL,
author = "Wen-Chen Chen",
title = "On {Zipf}'s law",
type = "Thesis ({Ph.D.})",
school = "University of Michigan",
address = "Ann Arbor, MI, USA",
pages = "114",
year = "1978",
MRclass = "Thesis",
MRnumber = "2627928",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:7822871",
acknowledgement = ack-nhfb,
remark = "Available from ProQuest LLC, Ann Arbor, MI, USA.
Author given name appears as Wen-Cheng in MathSciNet
database.",
}
@Article{Elshoff:1978:SSC,
author = "James L. Elshoff",
title = "A study of the structural composition of {PL/I}
programs",
journal = j-SIGPLAN,
volume = "13",
number = "6",
pages = "29--37",
month = jun,
year = "1978",
CODEN = "SINODQ",
DOI = "http://doi.acm.org/10.1145/987515.987518",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Wed Jun 18 16:08:52 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Some research on a theory of the structural
composition of an algorithm has recently been reported.
The theory embodies models of operator and operand
distributions that have been proposed by Bayer, Zipf,
and Zweben. This paper reports a study in which the
three models of operator distributions are compared
with the measured distributions found in 34 PL/I
programs. Two of three models, one by Zipf and one by
Zweben, are shown to correlate highly with the measured
distributions. Two variations of the Zipf model are
then formulated and tested with good results. Also, the
relationship between the method of counting operators
and the models is investigated.",
acknowledgement = ack-nhfb,
classification = "C4240 (Programming and algorithm theory); C6140D
(High level languages)",
corpsource = "Computer Sci. Dept., General Motors Res. Labs.,
Warren, MI, USA",
fjournal = "ACM SIG{\-}PLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "counting operators; operator distributions; PL/1; PL/1
programs; programming theory; structural composition",
treatment = "T Theoretical or Mathematical",
}
@Book{Heaps:1978:IRC,
author = "Harold Stanley Heaps",
title = "Information retrieval, computational and theoretical
aspects",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xii + 344",
year = "1978",
ISBN = "0-12-335750-0",
ISBN-13 = "978-0-12-335750-2",
LCCN = "Z699 .H38",
bibdate = "Sat Nov 12 11:36:39 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Library and information science",
acknowledgement = ack-nhfb,
remark = "Heaps's Law is given on pp. 206--208.",
subject = "Information storage and retrieval systems",
}
@Article{Logan:1978:FDP,
author = "Jonothan L. Logan and Samuel A. Goudsmit",
title = "The First Digit Phenomenon",
journal = j-PROC-AMER-PHIL-SOC,
volume = "122",
number = "4",
pages = "193--197",
day = "18",
month = aug,
year = "1978",
CODEN = "PAPCAA",
ISSN = "0003-049X",
ISSN-L = "0003-049X",
bibdate = "Fri Mar 30 11:20:35 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This paper contains derivations of both Stigler's Law
and Benford's Law, and receives strong criticism in
\cite{Raimi:1985:FDP}. This paper contains an important
historical note that is recorded in entry
\cite{Benford:1938:LAN}.",
URL = "http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C;
http://www.jstor.org/stable/986530",
abstract = "Forty years ago an article appeared in these
Proceedings, which has since then attracted much
attention of mathematicians and some physicists. It was
written by Frank Benford, a physicist from the General
Electric Company at Schenectady. He had examined a
large number of numerical tables, the kind that are
printed in almanacs, and in scientific and technical
handbooks. He noticed a most unusual and unexpected
property of many of these tables. Consider, for
example, the numbers representing the populations of
states or all the countries in the world, or their
areas, their budgets, their numbers of hospital beds,
etc. One would expect that on the average just as many
of these entries would begin with the digit $1$ as with
$2$ or $3$ or $4$, and so on. But Benford noticed that
small values of the first digits occur far more
often.",
acknowledgement = ack-nhfb,
author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
remark = "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
the concept of electron spin, a critical step forward
in the quantum mechanics of many-electron systems.
Surprisingly, that work did not get them the Nobel
Prize, but it did spur Wolfgang Pauli to present his
Exclusion Principle in 1925, for which he received the
1945 Nobel Prize in Physics. After World War II,
Goudsmit was the scientific head of the Alsos mission
to capture German nuclear scientists. In the 1950s, he
founded the journal Physical Review Letters. During the
1960s and 1970s, he was Editor-in-Chief of the main
American physics journal, the Physical Review.",
}
@Article{Rouault:1978:LZS,
author = "Alain Rouault",
title = "Lois de {Zipf} et sources markoviennes. ({French})
[{Zipf}'s law and {Markovian} sources]",
journal = "Ann. Inst. H. Poincar{\'e} Sect. B (N.S.)",
volume = "14",
number = "2",
pages = "169--188",
year = "1978",
CODEN = "AHPBAR",
ISSN = "0020-2347",
ISSN-L = "0020-2347",
MRclass = "62E99 (60J20 62P99)",
MRnumber = "507732 (80c:62026a)",
MRreviewer = "Bruce M. Hill",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Annales de l'Institut Henri Poincar{\'e}. Section B.
Calcul des Probabilit{\'e}s et Statistique. Nouvelle
S{\'e}rie",
language = "French",
}
@Article{Samson:1978:STU,
author = "W. B. Samson and R. H. Davis",
title = "Search Times Using Hash Tables for Records with
Non-Unique Keys",
journal = j-COMP-J,
volume = "21",
number = "3",
pages = "210--214",
month = aug,
year = "1978",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/hash.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/210.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/211.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/212.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/213.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/214.tif",
abstract = "Recent research in hash coding has concentrated on
unique keys, or uniform distributions of keys. This
paper is intended to clarify the effect of non-unique
keys with various distributions on search times in the
hash table thus enabling recommendations to be made to
those who must deal with hash tables of this type. It
is found that extreme rank-order frequency distribution
of keys, such as the Zipf distribution, result in much
higher access times than more uniform distributions,
but it is possible to reduce these to some extent by
loading records with common keys on to the hash table
first.",
acknowledgement = ack-nhfb,
classcodes = "C6120 (File organisation); C6130 (Data handling
techniques)",
classification = "723",
corpsource = "Dept. of Math. and Computer Studies, Dundee Coll. of
Technol., Dundee, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
journalabr = "Comput J",
keywords = "common keys; compiler symbol; computer programming;
data handling; data processing --- Data Structures;
direct access files; distribution; extreme; file
organisation; hash tables; higher access times; non
unique keys; overflow method; rank order frequency
distribution of keys; records; search times;
simulation; tables; uniform distributions; Zipf",
treatment = "T Theoretical or Mathematical",
}
@Article{Diaconis:1979:RP,
author = "Persi Diaconis and David Freedman",
title = "On Rounding Percentages",
journal = j-J-AM-STAT-ASSOC,
volume = "74",
number = "366",
pages = "359--364",
month = jun,
year = "1979",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Nov 23 11:24:59 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
note = "The authors extend prior work on correctness of sums
of rounded percentages \cite{Mosteller:1967:DSR}, and
criticize biased rounding practices in
\cite{Benford:1938:LAN}.",
URL = "http://www.jstor.org/stable/2284288",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "Benford's Law",
remark = "When percentage-column entries are rounded, their sum
may differ from 100\%. The authors use a prior proof
\cite{Mosteller:1967:DSR} that for $ n \gg 2 $ rounded
values, the probability of a correct sum is $ \sqrt {6
/ (\pi n)} \approx 1.382 / \sqrt {n} $. They show that
rounding may produce large changes in computed
chi-squared values, and they conclude their article
with this recommendation: ``it is important to
calculate with many-digit accuracy when computing $
\chi^2 $ for large sample sizes.''",
}
@Article{Mohanty:1979:MMQ,
author = "Siba N. Mohanty",
title = "Models and Measurements for Quality Assessment of
Software",
journal = j-COMP-SURV,
volume = "11",
number = "3",
pages = "251--275",
month = sep,
year = "1979",
CODEN = "CMSVAN",
DOI = "http://doi.acm.org/10.1145/356778.356783",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Thu Jun 19 09:25:12 MDT 2008",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1979.bib;
http://www.acm.org/pubs/contents/journals/surveys/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See also \cite{Dunn:1980:SFW,Mohanty:1980:SFW}.",
acknowledgement = ack-nhfb,
annote = "Several software quality assessment methods which span
the software life cycle are discussed. The quality of a
system design can be estimated by measuring the system
entropy function or the system work function. The
quality improvement due to reconfiguration can be
determined by calculating system entropy loading
measures. Software science and Zipf's law are shown to
be useful for estimating program length and
implementation time.",
country = "USA",
date = "11/10/79",
descriptors = "Software; design; software engineering; reliability;
measurement; model; fundamentals in statistics;
performance evaluation;",
enum = "2189",
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
references = "65",
}
@Article{Radhakrishnan:1979:LLC,
author = "T. Radhakrishnan and R. Kernizan",
title = "{Lotka's Law} and Computer Science Literature",
journal = j-J-AM-SOC-INF-SCI,
volume = "30",
number = "1",
pages = "51--54",
month = jan,
year = "1979",
CODEN = "AISJB6",
DOI = "http://dx.doi.org/10.1002/asi.4630300109",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Nov 25 07:45:09 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
onlinedate = "6 September 2007",
remark = "This paper analyzes publication statistics from
Communications of the Association for Computing
Machinery (CACM) and in the Journal of the ACM
(JACM).",
}
@Article{Vlachy:1979:FDS,
author = "Jan Vlach{\'y}",
title = "Frequency Distribution of Scientific Performance: a
Bibliography of {Lotka's Law} and Related Phenomena",
journal = j-SCIENTOMETRICS,
volume = "1",
number = "1",
pages = "107--130",
month = sep,
year = "1979",
CODEN = "SCNTDX",
DOI = "http://dx.doi.org/10.1007/BF02016844",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Fri Nov 25 07:59:34 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007%2FBF02016844;
http://www.springerlink.com/content/0138-9130/",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
xxjournal = "Scientometrics, Bibliography Section",
}
@Article{Brookes:1980:FISa,
author = "Bertram C. Brookes",
title = "The foundations of information science. {Part I}.
{Philosophical} aspects",
journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE,
volume = "2",
number = "3--4",
pages = "125--133",
month = jun,
year = "1980",
CODEN = "JISCDI",
DOI = "http://dx.doi.org/10.1177/016555158000200302",
ISSN = "0165-5515 (print), 1741-6485 (electronic)",
ISSN-L = "0165-5515",
bibdate = "Mon Feb 25 10:36:18 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jis.sagepub.com/content/2/3-4/125.abstract",
acknowledgement = ack-nhfb,
fjournal = "Journal of Information Science, Principles and
Practice",
journal-URL = "http://jis.sagepub.com/",
keywords = "Anomalous Law of Numbers; Benford's Law",
}
@Article{Brookes:1980:FISb,
author = "Bertram C. Brookes",
title = "The foundations of information science. {Part II}.
{Quantitative} aspects: classes of things and the
challenge of human individuality",
journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE,
volume = "2",
number = "5",
pages = "209--221",
month = oct,
year = "1980",
CODEN = "JISCDI",
DOI = "http://dx.doi.org/10.1177/016555158000200502",
ISSN = "0165-5515 (print), 1741-6485 (electronic)",
ISSN-L = "0165-5515",
bibdate = "Mon Feb 25 11:01:20 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jis.sagepub.com/content/2/5/209.abstract",
acknowledgement = ack-nhfb,
fjournal = "Journal of Information Science, Principles and
Practice",
journal-URL = "http://jis.sagepub.com/",
keywords = "Anomalous Law of Numbers; Benford's Law",
}
@Article{Brookes:1980:FISc,
author = "Bertram C. Brookes",
title = "The foundations of information science. {Part III}.
{Quantitative} aspects: Objective maps and subjective
landscapes",
journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE,
volume = "2",
number = "6",
pages = "269--275",
month = dec,
year = "1980",
CODEN = "JISCDI",
DOI = "http://dx.doi.org/10.1177/016555158000200602",
ISSN = "0165-5515 (print), 1741-6485 (electronic)",
ISSN-L = "0165-5515",
bibdate = "Mon Feb 25 10:36:18 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jis.sagepub.com/content/2/6/269.abstract",
acknowledgement = ack-nhfb,
fjournal = "Journal of Information Science, Principles and
Practice",
journal-URL = "http://jis.sagepub.com/",
keywords = "Anomalous Law of Numbers; Benford's Law",
}
@Article{Chen:1980:WFZ,
author = "Wen Chen Chen",
title = "On the weak form of {Zipf}'s law",
journal = j-J-APPL-PROBAB,
volume = "17",
number = "3",
pages = "611--622",
year = "1980",
CODEN = "JPRBAM",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
MRclass = "62E10 (62F10)",
MRnumber = "580021 (81m:62021)",
MRreviewer = "Patrick L. Brockett",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/3212955",
ZMnumber = "Zbl 0435.60017",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Probability",
journal-URL = "http://www.jstor.org/journals/00219002.html;
http://projecteuclid.org/euclid.jap/",
}
@Article{Dunn:1980:SFW,
author = "Stanley Dunn",
title = "Surveyor's Forum: {Working} on Interpretations",
journal = j-COMP-SURV,
volume = "12",
number = "2",
pages = "255--255",
month = jun,
year = "1980",
CODEN = "CMSVAN",
DOI = "http://doi.acm.org/10.1145/356810.356817",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Thu Jun 19 09:27:10 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/surveys/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Mohanty:1979:MMQ,Mohanty:1980:SFW}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@Article{Leimkuhler:1980:EFB,
author = "Ferdinand F. Leimkuhler",
title = "An Exact Formulation of {Bradford's Law}",
journal = j-J-DOC,
volume = "36",
number = "4",
pages = "285--292",
month = "????",
year = "1980",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/eb026699",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:14:04 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "An exact, discrete formulation of Bradford's law
describing the distribution of articles in journals is
derived by showing that Bradford's law is a special
case of the Zipf--Mandelbrot `rank frequency' law. A
relatively simple method is presented for fitting the
model to empirical data and estimating the number of
journals and articles in a subject collection. This
method is demonstrated with an example application.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@Article{McKee:1980:POR,
author = "Arnold F. McKee",
title = "The {Pareto} Optimum: Reconcilable with Social
Thought?",
journal = "International Journal of Social Economics",
volume = "7",
number = "7",
pages = "366--375",
month = "????",
year = "1980",
CODEN = "ISLEBC",
DOI = "http://dx.doi.org/10.1108/eb013878",
ISSN = "0306-8293 (print), 1758-6712 (electronic)",
ISSN-L = "0306-8293",
bibdate = "Fri Nov 25 07:01:57 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Mohanty:1980:SFW,
author = "Siba Mohanty",
title = "Surveyor's Forum: {Working} on Interpretations",
journal = j-COMP-SURV,
volume = "12",
number = "2",
pages = "256--256",
month = jun,
year = "1980",
CODEN = "CMSVAN",
DOI = "http://doi.acm.org/10.1145/356810.356818",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Thu Jun 19 09:27:10 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/surveys/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Mohanty:1979:MMQ,Dunn:1980:SFW}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@Article{Brookes:1981:FIS,
author = "Bertram C. Brookes",
title = "The foundations of information science. {Part IV}.
{Information} science: the changing paradigm",
journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE,
volume = "3",
number = "1",
pages = "3--12",
month = feb,
year = "1981",
CODEN = "JISCDI",
DOI = "http://dx.doi.org/10.1177/016555158100300102",
ISSN = "0165-5515 (print), 1741-6485 (electronic)",
ISSN-L = "0165-5515",
bibdate = "Mon Feb 25 10:36:18 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jis.sagepub.com/content/3/1/3",
acknowledgement = ack-nhfb,
fjournal = "Journal of Information Science, Principles and
Practice",
journal-URL = "http://jis.sagepub.com/",
keywords = "Anomalous Law of Numbers; Benford's Law",
}
@Book{Fleiss:1981:SMR,
author = "Joseph L. Fleiss",
title = "Statistical Methods for Rates and Proportions",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Second",
pages = "xviii + 321",
year = "1981",
ISBN = "0-471-06428-9",
ISBN-13 = "978-0-471-06428-2",
LCCN = "QA279 .F58 1981",
bibdate = "Fri Mar 22 08:46:57 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Wiley series in probability and mathematical
statistics",
URL = "http://www.loc.gov/catdir/description/wiley032/80026382.html;
http://www.loc.gov/catdir/enhancements/fy0607/80026382-b.html;
http://www.loc.gov/catdir/toc/onix02/80026382.html",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
subject = "Analysis of variance; Sampling (Statistics);
Biometry",
}
@Article{Kennard:1981:MDF,
author = "Robert W. Kennard and John E. Reith",
title = "{M32}. On the distribution of first digits",
journal = j-COMMUN-STAT-SIMUL-COMPUT,
volume = "10",
number = "1",
pages = "97--98",
month = "????",
year = "1981",
CODEN = "CSSCDB",
DOI = "http://dx.doi.org/10.1080/03610918108812195",
ISSN = "0361-0918",
ISSN-L = "0361-0918",
bibdate = "Sat Jan 07 09:27:42 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/03610918108812195",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics: Simulation and
Computation",
keywords = "Benford's Law",
onlinedate = "27 Jun 2007",
}
@Article{Pavlov:1981:DFF,
author = "A. I. Pavlov",
title = "On the distribution of fractions and {F. Benford}'s
law",
journal = j-IZV-AKAD-NAUK-SSSR-MAT,
volume = "45",
number = "4",
pages = "760--774, 927",
year = "1981",
CODEN = "IZAMAT",
ISSN = "0373-2436",
ISSN-L = "0373-2436",
MRclass = "10K10",
MRnumber = "631437 (83m:10093)",
MRreviewer = "Michael Keane",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Izvestiia Akademii Nauk. USSR Seriia Matematicheskaia
(Moscow)",
xxtitle = "On the distribution mod one and {Benford}'s law",
}
@Article{Peters:1981:EFB,
author = "James V. Peters",
title = "An Equivalent Form of {Benford's Law}",
journal = j-FIB-QUART,
volume = "19",
number = "1",
pages = "74--76",
month = feb,
year = "1981",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
MRclass = "60C05 (10K10 60-01)",
MRnumber = "606117 (82k:60024)",
MRreviewer = "L. E. Clarke",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.fq.math.ca/19-1.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/19-1/peters.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Peters:1981:SCC,
author = "James V. Peters",
title = "Short Communications: a combinatoric proof of
{Benford}'s law",
journal = j-AEQUATIONES-MATHEMATICAE,
volume = "23",
number = "1",
pages = "122--123",
year = "1981",
CODEN = "AEMABN",
DOI = "http://dx.doi.org/10.1007/BF02188018",
ISSN = "0001-9054",
ISSN-L = "0001-9054",
MRclass = "Contributed Item",
MRnumber = "1553878",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/accesspage/article/10.1007/BF02188018",
acknowledgement = ack-nhfb,
fjournal = "Aequationes Mathematicae",
journal-URL = "http://link.springer.com/journal/10",
}
@Article{Potter:1981:LLR,
author = "William Gray Potter",
title = "{Lotka's Law} revisited",
journal = j-LIBR-TRENDS,
volume = "31",
number = "2",
pages = "21--39",
month = "Summer",
year = "1981",
CODEN = "LIBTA3",
ISSN = "0024-2594",
ISSN-L = "0024-2594",
bibdate = "Thu Nov 24 14:41:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.172.9842",
acknowledgement = ack-nhfb,
fjournal = "Library Trends",
}
@Article{Preece:1981:DFD,
author = "D. A. Preece",
title = "Distributions of Final Digits in Data",
journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN,
volume = "30",
number = "1",
pages = "31--60",
month = mar,
year = "1981",
ISSN = "0039-0526 (print), 1467-9884 (electronic)",
ISSN-L = "0039-0526",
bibdate = "Wed Nov 23 12:19:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2987702",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series D
(The Statistician)",
remark = "This paper extends previous work \cite{Yule:1927:RS}
on human bias in the recording of last digits in
measurements, or from roundings, or from later scale
conversions, and how such bias can be detected.",
}
@Article{Schatte:1981:RVL,
author = "Peter Schatte",
title = "On random variables with logarithmic mantissa
distribution relative to several bases",
journal = j-ELEK-INFO-KYBER,
volume = "17",
number = "??",
pages = "293--295",
month = "????",
year = "1981",
CODEN = "EIVKAX",
ISSN = "0013-5712",
ISSN-L = "0013-5712",
bibdate = "Sat Nov 12 15:53:03 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Elektronische Informationsverarbeitung und Kybernetik
(EIK)",
}
@Article{Washington:1981:BLF,
author = "Lawrence C. Washington",
title = "{Benford's Law} for {Fibonacci} and {Lucas} Numbers",
journal = j-FIB-QUART,
volume = "19",
number = "2",
pages = "175--177",
month = apr,
year = "1981",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
MRclass = "10A30 (10A35)",
MRnumber = "614056 (82f:10009)",
MRreviewer = "S. P. Mohanty",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.fq.math.ca/19-2.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/19-2/washington.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Fedorowicz:1982:TFZ,
author = "Jane Fedorowicz",
title = "The Theoretical Foundation of {Zipf's Law} and Its
Application to the Bibliographic Database Environment",
journal = j-J-AM-SOC-INF-SCI,
volume = "33",
number = "5",
pages = "285--293",
year = "1982",
CODEN = "AISJB6",
DOI = "http://dx.doi.org/10.1002/asi.4630330507",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
}
@Article{Lefort:1982:LOA,
author = "B. Lefort",
title = "{L}'Emploi des Outils au Cours de Taches d'Entretien
et la Loi de {Zipf--Mandelbrot}. ({French}) [The Use of
Tools in Maintenance Tasks and the {Zipf--Mandelbrot
Law}]",
journal = j-TRAV-HUM,
volume = "45",
number = "2",
pages = "307--316",
month = "????",
year = "1982",
CODEN = "TRHUAH",
ISSN = "0041-1868 (print), 2104-3663 (electronic)",
ISSN-L = "0041-1868",
bibdate = "Mon Sep 10 07:17:32 MDT 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/40657805",
acknowledgement = ack-nhfb,
fjournal = "Le Travail Humain",
language = "French",
}
@Article{Pavlov:1982:DFP,
author = "A. I. Pavlov",
title = "On the Distribution of Fractional Parts and {Benford's
Law}",
journal = "Mathematics of the {USSR}-Izvestiya",
volume = "19",
number = "1",
pages = "65--77",
month = "????",
year = "1982",
CODEN = "????",
DOI = "http://dx.doi.org/10.1070/IM1982v019n01ABEH001411",
ISSN = "0025-5726",
ISSN-L = "0025-5726",
bibdate = "Sun Nov 13 10:46:55 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://stacks.iop.org/0025-5726/19/i=1/a=A05",
abstract = "This article investigates the distribution of the
first digits (from the left) in the $q$-nary expansions
of numerical sequences and functions ($q$ an integer $
\geq 2 $ )",
acknowledgement = ack-nhfb,
}
@PhdThesis{Perline:1982:EVM,
author = "Richard K. Perline",
title = "An extreme value model of weakly harmonic
({Pareto--Zipf} type) laws",
type = "Thesis ({Ph.D.})",
school = "Department of Behavioral Sciences, The University of
Chicago",
address = "Chicago, IL, USA",
pages = "129",
month = dec,
year = "1982",
MRnumber = "2611828",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://search.proquest.com/docview/251796701",
acknowledgement = ack-nhfb,
remark = "Available from ProQuest LLC, Ann Arbor, MI, USA.",
}
@Article{Regazzini:1982:BFL,
author = "Eugenio Regazzini",
title = "The {Benford--Furlan} law as a statistical law",
journal = j-STATISTICA-BOLOGNA,
volume = "42",
number = "3",
pages = "351--370",
year = "1982",
CODEN = "STATDJ",
ISSN = "0390-590X (print), 1973-2201 (electronic)",
ISSN-L = "0390-590X",
MRclass = "62E99 (10K05 62A15)",
MRnumber = "695467 (84h:62032)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Statistica (Bologna)",
}
@Article{Turner:1982:DLS,
author = "Peter R. Turner",
title = "The distribution of leading significant digits",
journal = j-IMA-J-NUMER-ANAL,
volume = "2",
number = "4",
pages = "407--412",
month = oct,
year = "1982",
CODEN = "IJNADH",
DOI = "http://dx.doi.org/10.1093/imanum/2.4.407",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65G99 (60E05)",
MRnumber = "84f:65038",
MRreviewer = "Seppo Linnainmaa",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Book{Weaver:1982:LLT,
author = "Warren Weaver",
title = "{Lady Luck}: the theory of probability",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "392",
year = "1982",
ISBN = "0-486-24342-7",
ISBN-13 = "978-0-486-24342-9",
LCCN = "QA273 .W4 1982",
bibdate = "Mon Nov 14 11:35:17 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/description/dover031/82007396.html",
acknowledgement = ack-nhfb,
author-dates = "1894--1978",
remark = "Reprint of \cite{Weaver:1963:LLT}.",
subject = "Probabilities",
}
@Article{White:1982:FSS,
author = "Warren H. White",
title = "On the form of steady-state solutions to the
coagulation equations",
journal = j-J-COLLOID-INTERFACE-SCI,
volume = "87",
number = "1",
pages = "204--208",
month = may,
year = "1982",
CODEN = "JCISA5",
DOI = "http://dx.doi.org/10.1016/0021-9797(82)90382-4",
ISSN = "0021-9797 (print), 1095-7103 (electronic)",
ISSN-L = "0021-9797",
bibdate = "Thu Feb 28 10:46:13 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021979782903824",
acknowledgement = ack-nhfb,
fjournal = "Journal of Colloid and Interface Science",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Iyengar:1983:SPL,
author = "S. Sitharama Iyengar and A. K. Rajagopal and V. R. R.
Uppuluri",
title = "String patterns of leading digits",
journal = j-APPL-MATH-COMP,
volume = "12",
number = "4",
pages = "321--337",
month = jul,
year = "1983",
CODEN = "AMHCBQ",
DOI = "http://dx.doi.org/10.1016/0096-3003(83)90045-0",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Feb 16 18:02:26 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/science/journal/00963003",
URL = "http://www.sciencedirect.com/science/article/pii/0096300383900450",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Montroll:1983:NOD,
author = "Elliott W. Montroll and Michael F. Shlesinger",
title = "On $ 1 / f $ noise and other distributions with long
tails",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "79",
number = "10",
pages = "3380--3383",
day = "15",
month = may,
year = "1983",
CODEN = "PNASA6",
DOI = "http://dx.doi.org/10.1073/pnas.79.10.3380",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Thu Feb 28 11:03:24 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.pnas.org/content/79/10/3380.abstract",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Orlov:1983:SSZ,
author = "Yu. K. Orlov and R. Ya. Chitashvili",
title = "The statistical significance of {Zipf}'s
distribution",
journal = "Soobshch. Akad. Nauk Gruzin. SSR",
volume = "109",
number = "3",
pages = "505--508",
year = "1983",
CODEN = "????",
ISSN = "0132-1447",
ISSN-L = "0132-1447",
MRclass = "62E99 (62P99)",
MRnumber = "723296",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Soobshcheniya Akademii Nauk Gruzinsko{\u\i} SSR",
}
@Article{Schatte:1983:AUD,
author = "Peter Schatte",
title = "On the asymptotic uniform distribution of sums reduced
$ \bmod 1 $",
journal = j-MATH-NACHR,
volume = "115",
number = "1",
pages = "257--281",
month = "????",
year = "1983",
CODEN = "MTMNAQ",
DOI = "http://dx.doi.org/10.1002/mana.19841150121",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
bibdate = "Sat Feb 16 19:12:20 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1002/mana.19841150121/abstract",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
}
@Article{Schatte:1983:SUD,
author = "Peter Schatte",
title = "On {$ H_\infty $}-summability and the uniform
distribution of sequences",
journal = j-MATH-NACHR,
volume = "113",
number = "1",
pages = "237--243",
month = "????",
year = "1983",
CODEN = "MTMNAQ",
DOI = "http://dx.doi.org/10.1002/mana.19831130122",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
bibdate = "Sat Feb 16 19:13:27 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1002/mana.19831130122/abstract",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
}
@Article{Whittaker:1983:SID,
author = "James V. Whittaker",
title = "On Scale-Invariant Distributions",
journal = j-SIAM-J-APPL-MATH,
volume = "43",
number = "2",
pages = "257--267",
month = apr,
year = "1983",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
MRclass = "60E05 (10K10 62E10)",
MRnumber = "84h:60035",
MRreviewer = "K. C. Chanda",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
JSTOR database",
acknowledgement = ack-nhfb,
affiliation = "Univ of British Columbia, Dep of Mathematics,
Vancouver, BC, Can",
classification = "922",
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
journalabr = "SIAM J Appl Math",
keywords = "probability",
}
@Article{Bennett:1984:ZLS,
author = "J. M. Bennett",
title = "{Zipf's Law}, Structured Programming and Creativity",
journal = j-AUSTRALIAN-COMP-J,
volume = "16",
number = "4",
pages = "122--129",
year = "1984",
CODEN = "ACMJB2",
ISSN = "0004-8917",
ISSN-L = "0004-8917",
bibdate = "Fri Mar 9 17:59:26 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "As software projects increase in size, the effort
required to implement them increases at a greater rate.
The use of higher level languages and adherence to
various rules of ``good programming practice'' appear
to help only marginally in reducing the impact of this
non-linear effect, and progress can only be made by
calling on techniques for managing complexity which
have emerged in other fields. Hierarchical structures
are discussed with particular reference to software as
is the effect which appears to be common to a wide
range of human activities, and which is known as Zipf's
law. The effects of variation in individual programming
skills, the roles of creativity, invention and
innovation and lessons to be learned from case studies
of past failure are also examined.",
acknowledgement = ack-nhfb,
fjournal = "Australian Computer Journal",
keywords = "creativity; innovation; invention; large software
projects; project failures; structured programming;
Zipf's law",
}
@Article{Boroda:1984:ZML,
author = "M. G. Boroda and A. A. Polikarpov",
title = "The {Zipf--Mandelbrot} law and units of different
levels of text organization",
journal = "Tartu Riikl. {\"U}l. Toimetised",
volume = "??",
number = "689",
pages = "35--60",
year = "1984",
CODEN = "????",
ISSN = "????",
MRclass = "92A25",
MRnumber = "781731 (86c:92030)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Tartu Riikliku {\"U}likooli Toimetised. Uchenye
Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta
et Commentationes Universitatis Tartuensis",
}
@Article{Brookes:1984:RTE,
author = "Bertram C. Brookes",
title = "Ranking techniques and the empirical log law",
journal = j-INFO-PROC-MAN,
volume = "20",
number = "1--2",
pages = "37--46",
month = "????",
year = "1984",
CODEN = "IPMADK",
DOI = "http://dx.doi.org/10.1016/0306-4573(84)90038-4",
ISSN = "0306-4573 (print), 1873-5371 (electronic)",
ISSN-L = "0306-4573",
bibdate = "Mon Feb 25 10:38:32 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0306457384900384",
acknowledgement = ack-nhfb,
fjournal = "Information Processing and Management",
keywords = "Anomalous Law of Numbers; Benford's Law",
}
@Article{Bunt:1984:MPL,
author = "Richard B. Bunt and Jennifer M. Murphy and Shikharesh
Majumdar",
title = "A measure of program locality and its application",
journal = j-SIGMETRICS,
volume = "12",
number = "3",
pages = "28--40",
month = aug,
year = "1984",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1031382.809311",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Thu Jun 26 11:00:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "Although the phenomenon of locality has long been
recognized as the single most important characteristic
of program behaviour, relatively little work has been
done in attempting to measure it. Recent work has led
to the development of an intrinsic measure of program
locality based on the Bradford--Zipf distribution.
Potential applications for such a measure are many, and
include the evaluation of program restructuring methods
(manual and automatic), the prediction of system
performance, the validation of program behaviour
models, and the enhanced understanding of the phenomena
that characterize program behaviour. A consideration of
each of these areas is given in connection with the
proposed measure, both to increase confidence in the
validity of the measure and to illustrate a methodology
for dealing with such problems.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
journal-URL = "http://portal.acm.org/toc.cfm?id=J618",
}
@Article{Cohen:1984:PNF,
author = "D. I. A. Cohen and T. M. Katz",
title = "Prime numbers and the first digit phenomenon",
journal = j-J-NUMBER-THEORY,
volume = "18",
number = "3",
pages = "261--268",
month = jun,
year = "1984",
CODEN = "JNUTA9",
DOI = "http://dx.doi.org/10.1016/0022-314X(84)90061-1",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Fri Nov 25 13:58:58 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Number Theory",
}
@Article{Fedorowicz:1984:DEU,
author = "Jane Fedorowicz",
title = "Database evaluation using multiple regression
techniques",
journal = j-SIGMOD,
volume = "14",
number = "2",
pages = "70--76",
year = "1984",
CODEN = "SRECD8",
ISBN = "0-89791-128-8",
ISBN-13 = "978-0-89791-128-3",
ISSN = "0163-5808 (print), 1943-5835 (electronic)",
ISSN-L = "0163-5808",
bibdate = "Mon Dec 9 07:58:51 MST 1996",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "A model of the inverted file of an automated
bibliographic system is constructed using the Zipf
distribution of word frequency. By ascertaining the
parameters of the Zipfian model of the inverted file
system, one can estimate the minimum data storage
requirements of the database. In addition, given a few
additional system parameters, access time for a
specified query can be estimated. The estimation
procedures are accomplished using logarithmic
transformations and multiple regression techniques.
This paper introduces the Zipfian models, their
regression formulation, and their results and
interpretation for application to database
evaluation.",
acknowledgement = ack-nhfb,
affiliation = "Northwestern Univ, Kellogg Graduate Sch of Management,
Evanston, IL, USA",
affiliationaddress = "Northwestern Univ, Kellogg Graduate Sch of
Management, Evanston, IL, USA",
classification = "723; 901; 922",
conference = "SIGMOD '84, Proceedings of Annual Meeting (ACM Special
Interest Group on Management of Data).",
fjournal = "SIGMOD Record (ACM Special Interest Group on
Management of Data)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J689",
keywords = "access time model; bibliographic techniques; database
systems; evaluation; information storage systems;
mathematical models; multiple regression techniques;
Zipfian model",
meetingaddress = "Boston, MA, USA",
sponsor = "ACM, Special Interest Group on Management of Data, New
York, NY, USA",
}
@Article{Friedberg:1984:DFD,
author = "Steven H. Friedberg",
title = "The distribution of first digits",
journal = j-COLLEGE-MATH-J,
volume = "15",
number = "2",
pages = "120--125",
month = mar,
year = "1984",
ISSN = "0746-8342 (print), 1931-1346 (electronic)",
ISSN-L = "0746-8342",
bibdate = "Sat Feb 16 17:38:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2686516",
acknowledgement = ack-nhfb,
fjournal = "College Mathematics Journal",
}
@Article{Fuchs:1984:PDP,
author = "A. Fuchs and G. Letta",
title = "{Sur le probl{\`e}me du premier chiffre d{\'e}cimal}.
({French}) [{On} the problem of the first decimal
digit]",
journal = "{Bollettino della Unione Matem{\`a}tica Italiana.
Serie VI. B}",
volume = "3",
pages = "451--461",
year = "1984",
ISSN = "0392-4041",
ISSN-L = "0392-4041",
bibdate = "Wed Aug 12 10:09:50 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0557.60011",
acknowledgement = ack-nhfb,
ajournal = "Boll. Unione Mat. Ital., VI. Ser., B",
keywords = "analytical density; asymptotic density; first-digit
problem",
language = "French",
ZMclass = "60B99 (Probability theory on general structures)",
ZMreviewer = "R. Scozzafava",
}
@Article{Kohyama:1984:TIC,
author = "Tamotsu Kohyama and Y{\=o}ji Aizawa",
title = "Theory of the intermittent chaos. {$ 1 / f $} spectrum
and the {Pareto--Zipf} law",
journal = j-PROG-THEOR-PHYS,
volume = "71",
number = "5",
pages = "917--929",
year = "1984",
CODEN = "PTPKAV",
DOI = "http://dx.doi.org/10.1143/PTP.71.917",
ISSN = "0033-068X (print), 1347-4081 (electronic)",
ISSN-L = "0033-068X",
MRclass = "58F13 (76F99)",
MRnumber = "756214 (86a:58063)",
MRreviewer = "Joseph Ford",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Progress of Theoretical Physics",
}
@Article{Maia:1984:UBL,
author = "M. J. F. Maia and M. D. Maia",
title = "On the Unity of {Bradford's Law}",
journal = j-J-DOC,
volume = "40",
number = "3",
pages = "206--216",
month = "????",
year = "1984",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/eb026765",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:11:46 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@Article{McLaughlin:1984:DFI,
author = "William I. McLaughlin and Sylvia A. Lundy",
title = "Digit Functions of Integer Sequences",
journal = j-FIB-QUART,
volume = "22",
number = "2",
pages = "105--115",
month = may,
year = "1984",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:00:30 MDT 2011",
bibsource = "http://www.fq.math.ca/22-2.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/22-2/mclaughlin.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Nagasaka:1984:BL,
author = "Kenji Nagasaka",
title = "On {Benford}'s law",
journal = j-ANN-INST-STAT-MATH-TOKYO,
volume = "36",
number = "1",
pages = "337--352",
month = "????",
year = "1984",
CODEN = "AISXAD",
DOI = "http://dx.doi.org/10.1007/BF02481974",
ISSN = "0020-3157 (print), 1572-9052 (electronic)",
ISSN-L = "0020-3157",
MRclass = "60F99 (11K06 11K36 62E99)",
MRnumber = "758506 (86a:60052)",
MRreviewer = "L. Kuipers",
bibdate = "Sat Jan 31 18:19:56 MST 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/anninststatmath.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/BF02481974",
acknowledgement = ack-nhfb,
ajournal = "Ann. Inst. Statist. Math.",
fjournal = "Annals of the Institute of Statistical Mathematics
(Tokyo)",
journal-URL = "http://link.springer.com/journal/10463",
}
@Article{Schatte:1984:AUD,
author = "Peter Schatte",
title = "On the asymptotic uniform distribution of sums reduced
$ \bmod 1 $",
journal = j-MATH-NACHR,
volume = "115",
number = "1",
pages = "275--281",
month = "????",
year = "1984",
CODEN = "MTMNAQ",
DOI = "http://dx.doi.org/10.1002/mana.19841150121",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
bibdate = "Sat Nov 12 15:54:14 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1002/mana.19841150121/abstract",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
}
@Article{Turner:1984:FRD,
author = "Peter R. Turner",
title = "Further revelations on l.s.d",
journal = j-IMA-J-NUMER-ANAL,
volume = "4",
number = "2",
pages = "225--231",
month = apr,
year = "1984",
CODEN = "IJNADH",
DOI = "http://dx.doi.org/10.1093/imanum/4.2.225",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65G10 (11K99)",
MRnumber = "85m:65039",
MRreviewer = "Calvin T. Long",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
abstract = "In a recent paper the author showed that the
distribution of leading significant digits, l.s.d.,
resulting from successive multiplications is
logarithmic. In this paper these results are extended
by establishing, still without any assumptions of
invariance to scaling, that this distribution remains
invariant under all further arithmetic operations ---
both multiplicative and additive. The fact that 30\% of
decimal numbers have l.s.d. 1 persists.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "l. s. d. (leading significant digits)",
}
@Article{Yuan:1984:LOC,
author = "Y. Yuan",
title = "On the least {$Q$}-order of convergence of variable
metric algorithms",
journal = j-IMA-J-NUMER-ANAL,
volume = "4",
number = "2",
pages = "233--239",
month = apr,
year = "1984",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65K05",
MRnumber = "85h:65133",
MRreviewer = "A. I. \c Schiop",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Barlow:1985:RED,
author = "J. L. Barlow and E. H. Bareiss",
title = "On Roundoff Error Distributions in Floating Point and
Logarithmic Arithmetic",
journal = j-COMPUTING,
volume = "34",
number = "4",
pages = "325--347",
month = dec,
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05",
MRnumber = "87c:65045",
MRreviewer = "N. N. Abdelmalek",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
affiliation = "Pennsylvania State Univ, Computer Science Dep,
University Park, PA, USA",
affiliationaddress = "USA",
classification = "723",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "computer arithmetic; computer metatheory; floating
point arithmetic; logarithmic arithmetic; roundoff
error distributions",
}
@Article{Bradford:1985:SIS,
author = "Samuel C. Bradford",
title = "Sources of Information on Specific Subjects",
journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE,
volume = "10",
number = "4",
pages = "173--180",
month = oct,
year = "1985",
CODEN = "JISCDI",
ISSN = "0165-5515 (print), 1741-6485 (electronic)",
ISSN-L = "0165-5515",
bibdate = "Fri Nov 25 11:49:58 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Reprint of \cite{Bradford:1934:SIS}, the source of
Bradford's Law.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Information Science, Principles and
Practice",
journal-URL = "http://jis.sagepub.com/",
}
@Article{Egghe:1985:CLL,
author = "L. Egghe",
title = "Consequences of {Lotka's Law} for the {Law of
Bradford}",
journal = j-J-DOC,
volume = "41",
number = "3",
pages = "173--189",
month = "????",
year = "1985",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/eb026780",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:23:22 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
keywords = "Bradford's Law",
}
@Article{Faber:1985:AML,
author = "Vance Faber and Andrew B. {White, Jr.} and G. Milton
Wing",
title = "Analysis of a model that leads to the {Pareto} law of
wealth distribution",
journal = j-J-MATH-ANAL-APPL,
volume = "112",
number = "2",
pages = "579--594",
year = "1985",
CODEN = "JMANAK",
DOI = "http://dx.doi.org/10.1016/0022-247X(85)90264-1",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "90A14",
MRnumber = "813621 (87b:90027)",
bibdate = "Mon Feb 18 17:05:26 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
}
@Article{Lagarias:1985:PG,
author = "Jeffrey C. Lagarias",
title = "The $ 3 x + 1 $ Problem and Its Generalizations",
journal = j-AMER-MATH-MONTHLY,
volume = "92",
number = "1",
pages = "3--23",
month = jan,
year = "1985",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11K55 (11K31)",
MRnumber = "86i:11043",
MRreviewer = "A. D. Pollington",
bibdate = "Mon Jun 28 12:37:47 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
keywords = "Benford's Law",
}
@Article{Pao:1985:LLT,
author = "Miranda Lee Pao",
title = "{Lotka}'s law: a testing procedure",
journal = j-INFO-PROC-MAN,
volume = "21",
number = "4",
pages = "305--320",
month = "????",
year = "1985",
CODEN = "IPMADK",
DOI = "http://dx.doi.org/10.1016/0306-4573(85)90055-X",
ISSN = "0306-4573 (print), 1873-5371 (electronic)",
ISSN-L = "0306-4573",
bibdate = "Fri Nov 25 08:41:41 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing and Management",
}
@Article{Raimi:1985:FDP,
author = "R. Raimi",
title = "The First Digit Phenomenon Again",
journal = j-PROC-AMER-PHIL-SOC,
volume = "129",
number = "2",
pages = "211--219",
month = jun,
year = "1985",
CODEN = "PAPCAA",
ISSN = "0003-049X",
ISSN-L = "0003-049X",
bibdate = "Sat Nov 12 16:56:54 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This paper contains strong criticism of a derivation
of Benford's Law \cite{Logan:1978:FDP}.",
URL = "http://www.jstor.org/stable/986989",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
remark = "This paper contains mathematical derivations of both
Stigler's Law and Benford's Law. Raimi comments on p.
217: ``the Benford law itself as a conclusion to be
derived is by no means as firm as Kepler's planetary
curves. Indeed, it has been pointed out by Diaconis and
Freedman [D-F] [\cite{Diaconis:1979:RP}] that a
statistical analysis of Benford's announced data gives
a high probability to the conjecture that he did a bit
of rounding-off here and there, always in the direction
of his law. The license that a physicist often takes on
the path from his hypotheses to verified, observable,
and repeatable conclusion is not justified here.''.",
}
@Article{Tichy:1985:UDD,
author = "Robert F. Tichy",
title = "Uniform distribution and diophantine inequalities",
journal = j-MONAT-MATH,
volume = "99",
number = "2",
pages = "147--152",
month = jun,
year = "1985",
CODEN = "MNMTA2",
DOI = "http://dx.doi.org/10.1007/BF01304194",
ISSN = "0026-9255 (print), 1436-5081 (electronic)",
ISSN-L = "0026-9255",
bibdate = "Sun Feb 17 06:26:16 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/BF01304194",
ZMnumber = "0538.10039",
acknowledgement = ack-nhfb,
fjournal = "Monatshefte f{\"u}r Mathematik",
keywords = "diophantine inequalities; discrepancy; Uniformly
distributed sequences",
ZMclass = "11K06 (General theory of distribution modulo 1); 11D75
(Diophantine inequalities)",
}
@Article{Tuldava:1985:FST,
author = "Yu. A. Tuldava",
title = "The frequency structure of a text and {Zipf}'s law",
journal = "Tartu Riikl. {\"U}l. Toimetised",
volume = "??",
number = "711",
pages = "93--116",
year = "1985",
CODEN = "????",
ISSN = "????",
MRclass = "92A25 (94A15)",
MRnumber = "836129 (87c:92063)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Tartu Riikliku {\"U}likooli Toimetised. Uchenye
Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta
et Commentationes Universitatis Tartuensis",
}
@Article{Chen:1986:RBL,
author = "Ye-Sho Chen and Ferdinand F. Leimkuhler",
title = "A relationship between {Lotka's Law}, {Bradford's
Law}, and {Zipf's Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "37",
number = "5",
pages = "307--314",
year = "1986",
CODEN = "AISJB6",
DOI = "2-8;
http://dx.doi.org/10.1002/(SICI)1097-4571(198609)37:5<307::AID-ASI5>3.0.CO",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
}
@Article{Feldstein:1986:OUS,
author = "Alan Feldstein and Peter Turner",
title = "Overflow, underflow, and severe loss of significance
in floating-point addition and subtraction",
journal = j-IMA-J-NUMER-ANAL,
volume = "6",
number = "2",
pages = "241--251",
month = apr,
year = "1986",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65G05",
MRnumber = "89h:65065",
bibdate = "Sat Dec 23 14:52:49 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "In this paper it is shown that, under the assumption
of the logarithmic distribution of numbers,
floating-point addition and subtraction can result in
overflow or underflow with alarming frequency --- a
frequency that increases rapidly with machine speed
unless the range of the exponent is also increased. If
numbers are assumed to be distributed in accordance
with Sweeney's (1965) experiments, then severe loss of
significance occurs with large probability in floating
point subtraction. These results have implications for
computer design and lead to the suggestion of a long
word format which will reduce the risks to acceptable
levels.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "Benford's Law; Law of Anomalous Numbers; logarithmic
distribution; overflow; underflow; Zipf's Law",
}
@Article{Green:1986:BRP,
author = "M. W. Green",
title = "Book Reviews: {{\em Pareto Distributions}}, by {B. C.
Arnold}",
journal = j-APPL-STAT,
volume = "35",
number = "2",
pages = "215--215",
year = "1986",
CODEN = "APSTAG",
ISSN = "0035-9254 (print), 1467-9876 (electronic)",
ISSN-L = "0035-9254",
bibdate = "Sat Apr 21 10:24:36 MDT 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Applied Statistics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}
@Article{Hoare:1986:DFS,
author = "G. T. Q. Hoare and E. Wright",
title = "The distribution of first significant digits",
journal = j-MATH-GAZ,
volume = "70",
number = "451",
pages = "34--37",
month = mar,
year = "1986",
CODEN = "MAGAAS",
ISSN = "0025-5572",
ISSN-L = "0025-5572",
bibdate = "Sat Feb 16 17:57:52 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/3615826",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}
@Article{Katz:1986:FDP,
author = "Talbot M. Katz and Daniel I. A. Cohen",
title = "The First Digit Property for Exponential Sequences is
Independent of the Underlying Distribution",
journal = j-FIB-QUART,
volume = "24",
number = "1",
pages = "2--7",
month = feb,
year = "1986",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:00:45 MDT 2011",
bibsource = "http://www.fq.math.ca/24-1.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/24-1/katz.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Lemons:1986:NTD,
author = "Don S. Lemons",
title = "On the number of things and the distribution of first
digits",
journal = j-AMER-J-PHYSICS,
volume = "54",
number = "9",
pages = "816--817",
month = sep,
year = "1986",
CODEN = "AJPIAS",
DOI = "http://dx.doi.org/10.1119/1.14453",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Wed Nov 23 12:03:08 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://ajp.aapt.org/",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
keywords = "Benford's Law",
remark = "Lemons gives a derivation of Benford's Law that does
not assume scale invariance, unlike other widely-cited
derivations
\cite{Pinkham:1961:DFS,Raimi:1976:FDP,Raimi:1985:FDP}.",
}
@Book{Lines:1986:NYT,
author = "Malcolm E. Lines",
title = "A number for your thoughts: facts and speculations
about numbers from {Euclid} to the latest computers",
publisher = pub-ADAM-HILGER,
address = pub-ADAM-HILGER:adr,
pages = "vi + 214",
year = "1986",
ISBN = "0-85274-495-1 (paperback)",
ISBN-13 = "978-0-85274-495-6 (paperback)",
LCCN = "QA241 .L617 1986",
bibdate = "Wed Nov 23 11:34:02 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.gbv.de:20011/gvk",
URL = "http://www.loc.gov/catdir/enhancements/fy0668/86183277-d.html",
acknowledgement = ack-nhfb,
remark = "Chapter 7 (pp. 43--52) is entitled: ``The Baffling Law
of Benford''.",
subject = "number theory",
}
@Article{Patil:1986:DFD,
author = "S. A. Patil and V. R. R. Uppulari",
title = "The distribution of first $j$ digits",
journal = j-COLLEGE-MATH-J,
volume = "17",
number = "3",
pages = "240--243",
month = may,
year = "1986",
CODEN = "????",
ISSN = "0746-8342 (print), 1931-1346 (electronic)",
ISSN-L = "0746-8342",
bibdate = "Sat Feb 16 19:00:24 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2686982",
acknowledgement = ack-nhfb,
fjournal = "College Mathematics Journal",
keywords = "Benford's Law",
}
@Article{Schatte:1986:ALD,
author = "Peter Schatte",
title = "On the asymptotic logarithmic distribution of the
floating-point mantissas of sums",
journal = j-MATH-NACHR,
volume = "127",
number = "1",
pages = "7--20",
month = "????",
year = "1986",
CODEN = "MTMNAQ",
DOI = "http://dx.doi.org/10.1002/mana.19861270102",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
bibdate = "Sun Feb 17 06:04:23 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1002/mana.19861270102/abstract",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
}
@Article{Tichy:1986:GZU,
author = "Robert F. Tichy",
title = "{Gleichverteilung und zahlentheoretische Ungleichungen
II}. ({German}) [{Uniform} distribution and
number-theoretic inequalities {II}]",
journal = "Anzeiger der {\"O}sterreichischen Akademie der
Wissenschaften. Mathematisch-Naturwissenschaftliche
Klasse",
volume = "122(1985)",
number = "??",
pages = "95--99",
month = "????",
year = "1986",
CODEN = "OSAWA8",
DOI = "????",
ISSN = "0065-535X",
ISSN-L = "0065-535X",
bibdate = "Sun Feb 17 06:24:23 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "????",
acknowledgement = ack-nhfb,
ajournal = "Anz. {\"O}sterr. Akad. Wiss., Math.-Naturwiss. Kl.",
classmath = "11K06 (General theory of distribution modulo 1); 11J25
(Diophantine inequalities)",
keywords = "diophantine inequalities; discrepancy; H infinity;
logarithmic mean; summation method; uniform
distribution",
language = "German",
xxnote = "Despite repeated searches, I have not found this
journal online, not even from links at the Austrian
Academy of Sciences, \path=http://www.oeaw.ac.at=.",
}
@Article{Bak:1987:SOC,
author = "Per Bak and Chao Tang and Kurt Wiesenfeld",
title = "Self-organized criticality: An explanation of the $ 1
/ f $ noise",
journal = j-PHYS-REV-LET,
volume = "59",
number = "4",
pages = "381--384",
month = jul,
year = "1987",
CODEN = "PRLTAO",
DOI = "http://dx.doi.org/10.1103/PhysRevLett.59.381",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Thu Feb 28 10:54:26 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.59.381",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Chen:1987:AZL,
author = "Ye-Sho Chen and Ferdinand F. Leimkuhler",
title = "Analysis of {Zipf}'s law: An index approach",
journal = j-INFO-PROC-MAN,
volume = "23",
number = "3",
pages = "171--182",
day = "1",
month = apr,
year = "1987",
CODEN = "IPMADK",
DOI = "http://dx.doi.org/10.1016/0306-4573(87)90002-1",
ISSN = "0306-4573 (print), 1873-5371 (electronic)",
ISSN-L = "0306-4573",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0306457387900021",
ZMnumber = "0614.62150",
abstract = "A rigorous analysis of Zipf's law is made using an
index for the sequence of observed values of the
variables in a Zipf-type relationship. Three important
properties relating rank, count, and frequency are
identified. Using this approach, the shape of Zipf-type
curves can be described in terms of three distinct
regions and two parameters of the Mandelbrot--Zipf law.
This result has considerable practical significance,
since it provides rigorous foundations for the
application of Zipf's law.",
acknowledgement = ack-nhfb,
classmath = "62P99 (Appl. of statistics)",
fjournal = "Information Processing and Management",
keywords = "index approach; Mandelbrot-Zipf law; Zipf's law",
}
@Article{Fedorowicz:1987:DPE,
author = "Jane Fedorowicz",
title = "Database Performance Evaluation in an Indexed File
Environment",
journal = j-TODS,
volume = "12",
number = "1",
pages = "85--110",
month = mar,
year = "1987",
CODEN = "ATDSD3",
ISSN = "0362-5915 (print), 1557-4644 (electronic)",
ISSN-L = "0362-5915",
bibdate = "Sat Apr 14 10:34:48 MDT 2001",
bibsource = "Compendex database; Database/Graefe.bib;
Database/Wiederhold.bib; http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.acm.org/pubs/articles/journals/tods/1987-12-1/p85-fedorowicz/p85-fedorowicz.pdf;
http://www.acm.org/pubs/citations/journals/tods/1987-12-1/p85-fedorowicz/;
http://www.acm.org/pubs/toc/Abstracts/tods/13675.html",
abstract = "The use of database systems for managerial decision
making often incorporates information-retrieval
capabilities with numeric report generation. Of great
concern to the user of such a system is the response
time associated with issuing a query to the database.
This study presents a procedure for estimating response
time for one of the most frequently encountered
physical storage mechanisms, the indexed file. The
model provides a fairly high degree of accuracy, but is
simple enough so that the cost of applying the model is
not exorbitant. The model incorporates the knowledge
that the distribution of access key occurrences is
known to follow Zipf's law. It first estimates the
access time required to complete the query, which
includes the time needed for all input and output
transactions, and CPU time used in performing the
search. The effects of multiple users on an
individual's response time are then assessed using a
simple regression estimation technique. The two-step
procedure allows for the separation of access time from
multiuser influences.",
acknowledgement = ack-nhfb,
affiliation = "Boston Univ, Boston, MA, USA",
affiliationaddress = "Boston Univ, Boston, MA, USA",
annote = "a procedure for estimating response time; distribution
of access key occurrences follow Zipf's law. Early
version with Kellogg, J. L. Model provides a fairly
high degree of accuracy but is simple. The effects of
multiple users are assessed using simple regression
estimation.",
classification = "723; 912; 922",
fjournal = "ACM Transactions on Database Systems",
generalterms = "Design; Performance",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777",
keywords = "data processing --- File organization; database
performance; database systems; indexed file
environment; MANAGEMENT --- Information Systems;
multiple users, design; Performance; performance;
response time; statistical methods --- regression
analysis; Zipf's law",
subject = "{\bf D.4.3}: Software, OPERATING SYSTEMS, File Systems
Management, File organization. {\bf H.2.2}: Information
Systems, DATABASE MANAGEMENT, Physical Design, Access
methods. {\bf H.3.2}: Information Systems, INFORMATION
STORAGE AND RETRIEVAL, Information Storage, File
organization. {\bf H.3.3}: Information Systems,
INFORMATION STORAGE AND RETRIEVAL, Information Search
and Retrieval, Retrieval models.",
}
@Article{Hosking:1987:PQE,
author = "J. R. M. Hosking and J. R. Wallis",
title = "Parameter and Quantile Estimation for the Generalized
{Pareto} Distribution",
journal = j-TECHNOMETRICS,
volume = "29",
number = "3",
pages = "339--349",
month = "????",
year = "1987",
CODEN = "TCMTA2",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Fri Nov 25 16:39:38 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html;
http://www.tandfonline.com/loi/utch20",
}
@Article{Kunoff:1987:FDP,
author = "Sharon Kunoff",
title = "{$ N! $} has the First Digit Property",
journal = j-FIB-QUART,
volume = "25",
number = "4",
pages = "365--367",
month = nov,
year = "1987",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:01:00 MDT 2011",
bibsource = "http://www.fq.math.ca/25-4.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/25-4/kunoff.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Nagasaka:1987:BLL,
author = "Kenji Nagasaka and Jau-Shyong Shiue",
title = "{Benford}'s law for linear recurrence sequences",
journal = "Tsukuba J. Math.",
volume = "11",
number = "2",
pages = "341--351",
year = "1987",
CODEN = "????",
ISSN = "0387-4982",
ISSN-L = "0387-4982",
MRclass = "60E99 (11B37)",
MRnumber = "926460 (88m:60047)",
MRreviewer = "L. Kuipers",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Tsukuba Journal of Mathematics",
}
@Article{Nicholls:1987:EZP,
author = "Paul Travis Nicholls",
title = "Estimation of {Zipf} parameters",
journal = j-J-AM-SOC-INF-SCI,
volume = "38",
number = "6",
pages = "443--445",
year = "1987",
CODEN = "AISJB6",
DOI = "2-E;
http://dx.doi.org/10.1002/(SICI)1097-4571(198711)38:6<443::AID-ASI4>3.0.CO",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
}
@Article{Sanders:1987:PPUa,
author = "Robert Sanders",
title = "The {Pareto Principle}: Its Use and Abuse",
journal = "Journal of Consumer Marketing",
volume = "4",
number = "1",
pages = "47--50",
month = "????",
year = "1987",
CODEN = "????",
DOI = "http://dx.doi.org/10.1108/eb008188",
ISSN = "0736-3761",
ISSN-L = "0736-3761",
bibdate = "Fri Nov 25 06:56:30 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Sanders:1987:PPUb,
author = "Robert Sanders",
title = "The {Pareto Principle}: Its Use and Abuse",
journal = "Journal of Services Marketing",
volume = "1",
number = "2",
pages = "37--40",
month = "????",
year = "1987",
CODEN = "????",
DOI = "http://dx.doi.org/10.1108/eb024706",
ISSN = "0887-6045",
ISSN-L = "0887-6045",
bibdate = "Fri Nov 25 06:56:30 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Schatte:1987:ABM,
author = "Peter Schatte",
title = "On the asymptotic behaviour of the mantissa
distribution of sums",
journal = j-J-INFO-PROC-CYBERNETICS-EIK,
volume = "23",
number = "??",
pages = "353--360",
month = "????",
year = "1987",
CODEN = "JICYE5",
ISSN = "0863-0593",
ISSN-L = "0863-0593",
bibdate = "Sat Nov 12 15:58:50 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Inform. Process. Cybern. EIK",
fjournal = "Journal of Information Processing and Cybernetics:
EIK",
}
@Article{Schatte:1987:SEU,
author = "Peter Schatte",
title = "Some estimates of the {$ \mathcal {H}_\infty
$}-uniform distribution",
journal = j-MONAT-MATH,
volume = "103",
number = "3",
pages = "233--249",
month = sep,
year = "1987",
CODEN = "MNMTA2",
DOI = "http://dx.doi.org/10.1007/BF01364342",
ISSN = "0026-9255 (print), 1436-5081 (electronic)",
ISSN-L = "0026-9255",
bibdate = "Sat Nov 12 15:57:05 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/BF01364342",
acknowledgement = ack-nhfb,
fjournal = "Monatshefte f{\"u}r Mathematik",
}
@Article{Tague:1987:MVZ,
author = "Jean Tague and Paul Nicholls",
title = "The maximal value of a {Zipf} size variable: Sampling
properties and relationship to other parameters",
journal = j-INFO-PROC-MAN,
volume = "23",
number = "3",
pages = "155--170",
day = "7",
month = jun,
year = "1987",
CODEN = "IPMADK",
DOI = "http://dx.doi.org/10.1016/0306-4573(87)90001-X",
ISSN = "0306-4573 (print), 1873-5371 (electronic)",
ISSN-L = "0306-4573",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/030645738790001X",
acknowledgement = ack-nhfb,
fjournal = "Information Processing and Management",
keywords = "Zipf's Law",
}
@Article{Tichy:1987:GS,
author = "Robert F. Tichy",
title = "{Gleichverteilung zum Summierungsverfahren {$ H_\infty
$}}. ({German}) [{Uniform} distribution to the {$
H_\infty $} summation method]",
journal = j-MATH-NACHR,
volume = "131",
number = "??",
pages = "119--125",
month = "????",
year = "1987",
CODEN = "MTMNAQ",
DOI = "http://dx.doi.org/10.1002/mana.19871310112",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
bibdate = "Mon Feb 18 06:44:11 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "????",
ZMnumber = "0626.10044",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
keywords = "$H_\infty$-discrepancy; difference sequences; real
sequences; uniform distribution",
language = "German",
ZMclass = "11K06 (General theory of distribution modulo 1); 40J05
(Summability in abstract structures)",
ZMreviewer = "D. Leitmann",
}
@Article{Turner:1987:DDI,
author = "Peter R. Turner",
title = "The Distribution of l.s.d. and Its Implications for
Computer Design",
journal = j-MATH-GAZ,
volume = "71",
number = "455",
pages = "26--31",
month = mar,
year = "1987",
CODEN = "MAGAAS",
DOI = "http://dx.doi.org/10.2307/3616283",
ISSN = "0025-5572",
ISSN-L = "0025-5572",
bibdate = "Tue Oct 30 23:36:58 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "[l.s.d. = least significant digits]. The topic is
variously known as Benford's Law, the Law of Anomalous
Numbers, and Zipf's Law.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
keywords = "Benford's Law; Law of Anomalous Numbers; logarithmic
distribution; overflow; underflow; Zipf's Law",
}
@Article{Belevitch:1988:PQD,
author = "Vitold Belevitch",
title = "{{\`A}} propos de la queue de la distribution de
{Zipf}. ({French}) [{On} the tail of the {Zipf}
distribution]",
journal = "Ann. Soc. Sci. Bruxelles S{\'e}r. I",
volume = "102",
number = "3",
pages = "73--85 (1989)",
year = "1988",
CODEN = "ASSBAH",
ISSN = "0037-959X",
ISSN-L = "0037-959X",
MRclass = "92A90",
MRnumber = "1016850 (90g:92114)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Annales de la Societ{\'e} Scientifique de Bruxelles.
S{\'e}rie I. Sciences Math{\'e}matiques, Astronomiques
et Physiques",
language = "French",
}
@Article{Carslow:1988:AIN,
author = "C. Carslow",
title = "Anomalies in Income Numbers. {Evidence} of Goal
Oriented Behavior",
journal = j-ACCOUNT-REV,
volume = "63",
number = "2",
pages = "321--327",
month = apr,
year = "1988",
CODEN = "ACRVAS",
ISSN = "0001-4826 (print), 1558-7967 (electronic)",
ISSN-L = "0001-4826",
bibdate = "Sat Dec 10 11:19:33 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/248109",
acknowledgement = ack-nhfb,
fjournal = "The Accounting Review",
keywords = "Benford's Law",
remark = "This paper references neither Newcomb nor Benford, but
it uses their digit-frequency formula from
\cite{Feller:1966:IPT} to compare with data on revenues
of New Zealand companies.",
}
@Article{Hill:1988:RNG,
author = "Theodore Hill",
title = "Random number guessing and the first digit
phenomenon",
journal = j-PSYCHOL-REP,
volume = "62",
number = "3",
pages = "967--971",
month = jun,
year = "1988",
CODEN = "PYRTAZ",
DOI = "http://dx.doi.org/10.2466/pr0.1988.62.3.967",
ISSN = "0033-2941 (print), 1558-691X (electronic)",
ISSN-L = "0033-2941",
bibdate = "Fri Feb 15 06:41:31 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.amsciepub.com/doi/abs/10.2466/pr0.1988.62.3.967",
acknowledgement = ack-nhfb,
ajournal = "Psychol. rep.",
fjournal = "Psychological Reports",
}
@InCollection{Kanemitsu:1988:BLF,
author = "Shigeru Kanemitsu and Kenji Nagasaka and G{\'e}rard
Rauzy and Jau-Shyong Shiue",
booktitle = "Probability theory and mathematical statistics
({Kyoto}, 1986)",
title = "On {Benford}'s law: the first digit problem",
volume = "1299",
publisher = pub-SV,
address = pub-SV:adr,
pages = "158--169",
year = "1988",
DOI = "http://dx.doi.org/10.1007/BFb0078471",
MRclass = "11K06 (60E99)",
MRnumber = "935987 (89d:11059)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Lecture Notes in Math.",
acknowledgement = ack-nhfb,
}
@InCollection{Nicolis:1988:PBZ,
author = "John S. Nicolis",
booktitle = "Synergetics, order and chaos ({Madrid}, 1987)",
title = "On the parallel between {Zipf}'s law and {$ 1 / f $}
processes in chaotic systems possessing coexisting
attractors",
publisher = "World Sci. Publ.",
address = "Teaneck, NJ, USA",
pages = "723--734",
year = "1988",
MRclass = "58F13 (00A69)",
MRnumber = "1115922 (92g:58087)",
MRreviewer = "Dieter H. Mayer",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Prather:1988:CET,
author = "R. E. Prather",
title = "Comparison and Extension of Theories of {Zipf} and
{Halstead}",
journal = j-COMP-J,
volume = "31",
number = "3",
pages = "248--252",
month = jun,
year = "1988",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/248.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/249.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/250.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/251.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/252.tif",
acknowledgement = ack-nhfb,
affiliation = "Trinity Univ, San Antonio, TX, USA",
affiliationaddress = "Trinity Univ, San Antonio, TX, USA",
classcodes = "C6110B (Software engineering techniques)",
classification = "723",
corpsource = "Comput. and Inf. Sci., Trinity Univ., San Antonio, TX,
USA",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "behavioural psychology; computer programming; computer
software; empirical law; Halstead metrics; Halstead's
hypothesis; length estimates; Measurements;
probabilistic hypothesis; process; programming;
software engineering; software metrication; software
science; Zipf metrics; Zipf's law",
treatment = "T Theoretical or Mathematical",
}
@Article{Sanders:1988:PPU,
author = "Robert Sanders",
title = "The {Pareto Principle}: Its Use and Abuse",
journal = "Journal of Business \& Industrial Marketing",
volume = "3",
number = "2",
pages = "37--40",
month = "????",
year = "1988",
CODEN = "????",
DOI = "http://dx.doi.org/10.1108/eb006057",
ISSN = "0885-8624",
ISSN-L = "0885-8624",
bibdate = "Fri Nov 25 07:04:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Schatte:1988:ASC,
author = "Peter Schatte",
title = "On the Almost Sure Convergence of Floating-Point
Mantissas and {Benford's Law}",
journal = j-MATH-NACHR,
volume = "135",
number = "1",
pages = "79--83",
month = "????",
year = "1988",
CODEN = "MTMNAQ",
DOI = "http://dx.doi.org/10.1002/mana.19881350108",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
MRclass = "60F15 (11K31)",
MRnumber = "944219 (89g:60114)",
MRreviewer = "S. A. Book",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://onlinelibrary.wiley.com/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
onlinedate = "12 Nov 2006",
reviewer = "S. A. Book",
}
@Article{Schatte:1988:LIL,
author = "Peter Schatte",
title = "On a law of the iterated logarithm for sums {$ \bmod 1
$} with application to {Benford}'s law",
journal = j-PROBAB-THEORY-RELAT-FIELDS,
volume = "77",
number = "2",
pages = "167--178",
month = feb,
year = "1988",
CODEN = "PTRFEU",
DOI = "http://dx.doi.org/10.1007/BF00334035",
ISSN = "0178-8051 (print), 1432-2064 (electronic)",
ISSN-L = "0178-8051",
MRclass = "60F15 (11K31)",
MRnumber = "927235 (89b:60081)",
MRreviewer = "L. Kuipers",
bibdate = "Sun Apr 27 11:18:06 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/probab-theory-relat-fields.bib",
URL = "http://link.springer.com/article/10.1007/BF00334035",
acknowledgement = ack-nhfb,
fjournal = "Probability Theory and Related Fields",
journal-URL = "http://link.springer.com/journal/440",
}
@Article{Schatte:1988:MDC,
author = "Peter Schatte",
title = "On Mantissa Distribution in Computing and {Benford}'s
Law",
journal = j-J-INFO-PROC-CYBERNETICS-EIK,
volume = "24",
number = "9",
pages = "443--455",
month = "????",
year = "1988",
CODEN = "JICYE5",
ISSN = "0863-0593",
ISSN-L = "0863-0593",
MRclass = "60E05 (11K06 11K31 65G99)",
MRnumber = "984516 (90g:60016)",
MRreviewer = "F. Schweiger",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
fjournal = "Journal of Information Processing and Cybernetics:
EIK",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Schatte:1988:UDC,
author = "Peter Schatte",
title = "On the uniform distribution of certain sequences and
{Benford}'s law",
journal = j-MATH-NACHR,
volume = "136",
number = "1",
pages = "271--273",
year = "1988",
CODEN = "MTMNAQ",
DOI = "http://dx.doi.org/10.1002/mana.19881360119",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
MRclass = "11K06 (11K31)",
MRnumber = "952478 (89j:11075)",
MRreviewer = "O. P. Stackelberg",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://onlinelibrary.wiley.com/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
onlinedate = "11 Nov 2006",
}
@Article{Tichy:1988:SRC,
author = "Robert F. Tichy",
title = "{Statistische Resultate {\"u}ber computergerechte
Darstellungen von Zahlen}. ({German}) [Statistical
results on computer-oriented representations of
numbers]",
journal = "Anzeiger der {\"O}sterreichischen Akademie der
Wissenschaften. Mathematisch-Naturwissenschaftliche
Klasse",
volume = "1987",
number = "??",
pages = "1--8",
month = "????",
year = "1988",
CODEN = "OSAWA8",
DOI = "????",
ISSN = "0065-535X",
ISSN-L = "0065-535X",
bibdate = "Mon Feb 18 06:45:27 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "????",
ZMnumber = "0625.10041",
acknowledgement = ack-nhfb,
ajournal = "Anz. {\"O}sterr. Akad. Wiss., Math.-Naturwiss. Kl.",
language = "German",
xxnote = "Despite repeated searches, I have not found this
journal online, not even from links at the Austrian
Academy of Sciences, \path=http://www.oeaw.ac.at=.",
ZMclass = "11K16 (Normal numbers, etc.); 11J71 (Distribution
modulo one); 11K38 (Irregularities of distribution)",
}
@Article{Arnold:1989:BEP,
author = "Barry C. Arnold and S. James Press",
title = "{Bayesian} estimation and prediction for {Pareto}
data",
journal = j-J-AM-STAT-ASSOC,
volume = "84",
number = "408",
pages = "1079--1084",
month = "????",
year = "1989",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62F15 (62F10)",
MRnumber = "92f:62034",
bibdate = "Mon May 5 12:36:01 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Chen:1989:ZLT,
author = "Ye-Sho Chen",
title = "{Zipf}'s laws in text modeling",
journal = "International Journal of General Systems. Methodology,
Applications, Education",
volume = "15",
number = "3",
pages = "233--252",
year = "1989",
CODEN = "IJGSAX",
DOI = "http://dx.doi.org/10.1080/03081078908935048",
ISSN = "0308-1079, 1026-7492, 1563-5104",
ISSN-L = "0308-1079",
MRclass = "92A90",
MRnumber = "1015844",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Internat. J. Gen. Systems",
fjournal = "International Journal of General Systems. Methodology,
Applications, Education",
}
@Article{Family:1989:KDG,
author = "Fereydoon Family and Paul Meakin",
title = "Kinetics of droplet growth processes: Simulations,
theory, and experiments",
journal = j-PHYS-REV-A,
volume = "40",
number = "7",
pages = "3836--3854",
month = oct,
year = "1989",
CODEN = "PLRAAN",
DOI = "http://dx.doi.org/10.1103/PhysRevA.40.3836",
ISSN = "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
ISSN-L = "1050-2947",
bibdate = "Thu Feb 28 10:49:20 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevA.40.3836",
acknowledgement = ack-nhfb,
fjournal = "Physical Review A (Atomic, Molecular, and Optical
Physics)",
journal-URL = "http://pra.aps.org/browse",
}
@InProceedings{Kitsuregawa:1989:EBS,
author = "Masaru Kitsuregawa and Masaya Nakayama and Mikio
Takagi",
title = "The Effect of Bucket Size Tuning in the Dynamic Hybrid
{GRACE} Hash Join Method",
crossref = "Apers:1989:VLD",
pages = "257--266",
month = aug,
year = "1989",
CODEN = "VLDBDP",
bibdate = "Sat Jan 25 17:38:12 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/hash.bib",
abstract = "In this paper, we show detailed analysis and
performance evaluation of the Dynamic Hybrid GRACE Hash
Join Method (DHGH Method) when the tuple distribution
in buckets is unbalanced. The conventional Hash Join
Methods specify the tuple distribution in buckets
statically. However it may differ from estimation since
join operations are applied with selection operations.
When the tuple distribution in buckets is unbalanced,
the processing cost of join operation becomes more
costly than the ideal case when you use Hybrid Hash
Join Method (HH Method). On the other hand, when you
use the DHGH Method, the destaging buckets are selected
dynamically, gives the same performance as the ideal
case even if the tuple distribution in buckets is
unbalanced such as Zipf-like distributions.",
acknowledgement = ack-nhfb,
affiliation = "Univ of Tokyo",
affiliationaddress = "Tokyo, Jpn",
classification = "723",
journalabr = "Very Large Data Bases Int Conf Very Large Data Bases",
keywords = "Computer Metatheory --- Programming Theory; Computer
Programming --- Algorithms; Database Systems; Query
Processing; Relational; Relational Algebra; VLDB",
}
@Article{Lang:1989:UAB,
author = "Sheau-Dong Lang and James R. Driscoll and Jiann H.
Jou",
title = "A Unified Analysis of Batched Searching of Sequential
and Tree-Structured Files",
journal = j-TODS,
volume = "14",
number = "4",
pages = "604--618",
month = dec,
year = "1989",
CODEN = "ATDSD3",
ISSN = "0362-5915 (print), 1557-4644 (electronic)",
ISSN-L = "0362-5915",
MRclass = "68P10 (68P20)",
MRnumber = "1 073 204",
bibdate = "Sat Apr 14 10:34:48 MDT 2001",
bibsource = "Database/Graefe.bib; Database/Wiederhold.bib;
http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.acm.org/pubs/articles/journals/tods/1989-14-4/p604-lang/p604-lang.pdf;
http://www.acm.org/pubs/citations/journals/tods/1989-14-4/p604-lang/;
http://www.acm.org/pubs/toc/Abstracts/tods/76908.html",
abstract = "A direct and unified approach is used to analyze the
efficiency of batched searching of sequential and
tree-structured files. The analysis is applicable to
arbitrary search distributions, and closed-form
expressions are obtained for the expected batched
searching cost and savings. In particular, we consider
a search distribution satisfying Zipf's law for
sequential files and four types of uniform (random)
search distribution for sequential and tree-structured
files. These results unify and extend earlier research
on batched searching and estimating block accesses for
database systems.",
acknowledgement = ack-nhfb,
affiliation = "Central Florida Univ., Orlando, FL, USA",
annote = "closed-form expressions for the number of accesses
needed given arbitrary search distributions.",
fjournal = "ACM Transactions on Database Systems",
generalterms = "Algorithms; Design; Performance; Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777",
keywords = "algorithms; design; performance; theory",
subject = "{\bf H.3.3}: Information Systems, INFORMATION STORAGE
AND RETRIEVAL, Information Search and Retrieval, Search
process. {\bf H.3.2}: Information Systems, INFORMATION
STORAGE AND RETRIEVAL, Information Storage, File
organization. {\bf H.2.2}: Information Systems,
DATABASE MANAGEMENT, Physical Design, Access methods.",
}
@Article{Nicolis:1989:CDM,
author = "G. Nicolis and C. Nicolis and John S. Nicolis",
title = "Chaotic dynamics, {Markov} partitions, and {Zipf}'s
law",
journal = j-J-STAT-PHYS,
volume = "54",
number = "3--4",
pages = "915--924",
month = feb,
year = "1989",
CODEN = "JSTPSB",
DOI = "http://dx.doi.org/10.1007/BF01019781",
ISSN = "0022-4715 (print), 1572-9613 (electronic)",
ISSN-L = "0022-4715",
MRclass = "58F13 (58F14 58F20)",
MRnumber = "988565 (90b:58184)",
MRreviewer = "Shi Hai Li",
bibdate = "Thu Aug 28 18:40:55 MDT 2014",
bibsource = "http://link.springer.com/journal/10955;
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0022-4715&volume=54&issue=3;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jstatphys1980.bib",
URL = "http://link.springer.com/article/10.1007/BF01019781",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Physics",
journal-URL = "http://link.springer.com/journal/10955",
}
@Article{Nicolis:1989:PBZ,
author = "John S. Nicolis and Ichiro Tsuda",
title = "On the parallel between {Zipf}'s law and {$ 1 / f $}
processes in chaotic systems possessing coexisting
attractors",
journal = j-PROG-THEOR-PHYS,
volume = "82",
number = "2",
pages = "254--274",
year = "1989",
CODEN = "PTPKAV",
ISSN = "0033-068X (print), 1347-4081 (electronic)",
ISSN-L = "0033-068X",
MRclass = "58F13 (92K20)",
MRnumber = "1023357 (91d:58165)",
MRreviewer = "Nima Geffen",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Progress of Theoretical Physics",
}
@Article{Schatte:1989:MUD,
author = "Peter Schatte",
title = "On measures of uniformly distributed sequences and
{Benford}'s law",
journal = j-MONAT-MATH,
volume = "107",
number = "3",
pages = "245--256",
year = "1989",
CODEN = "MNMTA2",
DOI = "http://dx.doi.org/10.1007/BF01300347",
ISSN = "0026-9255 (print), 1436-5081 (electronic)",
ISSN-L = "0026-9255",
MRclass = "11K36 (60F99)",
MRnumber = "1008683 (90k:11097)",
MRreviewer = "Kazuo Goto",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Monatshefte f{\"u}r Mathematik",
}
@Article{Shanbhag:1989:BRBa,
author = "D. N. Shanbhag",
title = "Book Review: {{\booktitle{Pareto Distributions}}, by
B. C. Arnold}",
journal = j-J-R-STAT-SOC-SER-A-STAT-SOC,
volume = "152",
number = "2",
pages = "253--254",
month = "????",
year = "1989",
CODEN = "JSSAEF",
DOI = "http://dx.doi.org/10.2307/2982920",
ISSN = "0964-1998 (print), 1467-985X (electronic)",
ISSN-L = "0964-1998",
bibdate = "Sat Jan 24 15:13:38 MST 2015",
bibsource = "http://www.jstor.org/stable/i349642;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-a-1980.bib",
URL = "http://www.jstor.org/stable/2982920",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series A
(Statistics in Society)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-985X;
http://www.jstor.org/journals/09641998.html",
}
@Article{Shieh:1989:BZE,
author = "Yeung-Nan Shieh",
title = "The {Beckmann--Zipf} effect and plant location under
uniform pricing",
journal = j-ECONOM-LETT,
volume = "30",
number = "1",
pages = "89--92",
day = "1",
month = jan,
year = "1989",
CODEN = "ECLEDS",
DOI = "http://dx.doi.org/10.1016/0165-1765(89)90162-6",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
MRclass = "90A12 (90B05)",
MRnumber = "1010312",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0165176589901626",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
keywords = "Zipf's Law",
}
@Article{Thomas:1989:UPR,
author = "Jacob K. Thomas",
title = "Unusual patterns in reported earnings",
journal = j-ACCOUNT-REV,
volume = "59",
number = "4",
pages = "773--787",
month = oct,
year = "1989",
CODEN = "ACRVAS",
ISSN = "0001-4826 (print), 1558-7967 (electronic)",
ISSN-L = "0001-4826",
bibdate = "Fri Feb 15 06:49:18 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/247861",
acknowledgement = ack-nhfb,
fjournal = "The Accounting Review",
keywords = "Benford's Law; distribution of first digits;
distribution of second digits",
}
@Article{Xekalaki:1989:APY,
author = "E. Xekalaki and J. Panaretos",
title = "On the Association of the {Pareto} and the {Yule}
Distribution",
journal = j-THEORY-PROBAB-APPL,
volume = "33",
number = "1",
pages = "191--195",
month = "????",
year = "1989",
CODEN = "TPRBAU",
DOI = "http://dx.doi.org/10.1137/1133028",
ISSN = "0040-585X (print), 1095-7219 (electronic)",
ISSN-L = "0040-585X",
bibdate = "Tue Apr 1 10:40:04 MDT 2014",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/33/1;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib",
acknowledgement = ack-nhfb,
fjournal = "Theory of Probability and its Applications",
journal-URL = "http://epubs.siam.org/tvp",
onlinedate = "January 1989",
}
@Article{Katsikas:1990:CDG,
author = "A. A. Katsikas and J. S. Nicolis",
title = "Chaotic dynamics of generating {Markov} partitions and
linguistic sequences mimicking {Zipf}'s law",
journal = "Nuovo Cimento D (1)",
volume = "12",
number = "2",
pages = "177--195",
year = "1990",
CODEN = "NCSDDN",
DOI = "http://dx.doi.org/10.1007/BF02450454",
ISSN = "0392-6737 (print), 1826-9893 (electronic)",
ISSN-L = "0392-6737",
MRclass = "92A90 (58F13 92A08 94A15)",
MRnumber = "1049338 (90m:92114)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Societ{\`a} Italiana di Fisica. Il Nuovo Cimento. D.
Serie 1",
}
@InCollection{Nagasaka:1990:BLL,
author = "Kenji Nagasaka and Shigeru Kanemitsu and Jau-Shyong
Shiue",
booktitle = "Number theory, {Vol}.\ {I} ({Budapest}, 1987)",
title = "{Benford}'s law: the logarithmic law of first digit",
volume = "51",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "361--391",
year = "1990",
MRclass = "11K06",
MRnumber = "1058225 (92b:11048)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Colloq. Math. Soc. J{\'a}nos Bolyai",
acknowledgement = ack-nhfb,
}
@Article{Schatte:1990:BLC,
author = "Peter Schatte",
title = "On {Benford}'s law for continued fractions",
journal = j-MATH-NACHR,
volume = "148",
pages = "137--144",
year = "1990",
CODEN = "MTMNAQ",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
MRclass = "11K50 (11K06)",
MRnumber = "1127337 (92m:11077)",
MRreviewer = "Harald Niederreiter",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
}
@Book{Szekely:1990:PKN,
author = "G{\'a}bor J. Sz{\'e}kely",
title = "{Paradoxa: klassische und neue {\"U}berraschungen aus
Wahrscheinlichkeitsrechnung und mathematischer
Statistik}. (German) [{Paradoxes}: traditional and new
surprises in probability and mathematical statistics]",
publisher = "Deutsch",
address = "Thun, Switzerland",
pages = "239",
year = "1990",
ISBN = "3-87144-850-8",
ISBN-13 = "978-3-87144-850-8",
LCCN = "????",
bibdate = "Thu Nov 17 19:26:05 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.gbv.de:20011/gvk",
note = "Translation by Ulrike Leitner from the Hungarian
original.",
URL = "http://www.gbv.de/dms/hbz/toc/ht003363686.pdf;
http://www.zentralblatt-math.org/zmath/en/search/?an=0743.60004",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{VandenBroeck:1990:LFB,
author = "C. {Van den Broeck} and R. Kawai",
title = "Learning in feedforward {Boolean} networks",
journal = j-PHYS-REV-A,
volume = "42",
number = "??",
pages = "6210--??",
day = "15",
month = nov,
year = "1990",
CODEN = "PLRAAN",
DOI = "http://dx.doi.org/10.1103/PhysRevA.42.6210",
ISSN = "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
ISSN-L = "1050-2947",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevA.42.6210",
acknowledgement = ack-nhfb,
fjournal = "Physical Review A (Atomic, Molecular, and Optical
Physics)",
journal-URL = "http://pra.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Yeh:1990:ODT,
author = "Hsiaw-Chan Yeh",
title = "One discrete time series model for fat-tailed integer
random variables: {Zipf} process",
journal = "Bulletin of the Institute of Mathematics. Academia
Sinica",
volume = "18",
number = "1",
pages = "19--33",
year = "1990",
CODEN = "BIMSDG",
ISSN = "0304-9825",
ISSN-L = "0304-9825",
MRclass = "60J10 (62M10)",
MRnumber = "1072827 (91i:60175)",
MRreviewer = "Ed McKenzie",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Bull. Inst. Math. Acad. Sinica",
fjournal = "Bulletin of the Institute of Mathematics. Academia
Sinica",
}
@Article{Antonini:1991:NUD,
author = "Rita Giuliano Antonini",
title = "On the Notion of Uniform Distribution Mod $1$",
journal = j-FIB-QUART,
volume = "29",
number = "3",
pages = "230--234",
month = aug,
year = "1991",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:01:34 MDT 2011",
bibsource = "http://www.fq.math.ca/29-3.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/29-3/antonini.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
keywords = "Benford's Law",
}
@Article{Burke:1991:BLP,
author = "John Burke and Eric Kincanon",
title = "{Benford}'s law and physical constants: The
distribution of initial digits",
journal = j-AMER-J-PHYSICS,
volume = "59",
number = "10",
pages = "952--952",
month = oct,
year = "1991",
CODEN = "AJPIAS",
DOI = "http://dx.doi.org/10.1119/1.16838",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Mon Nov 14 17:31:11 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/1991AmJPh..59..952B;
http://ajp.aapt.org/resource/1/ajpias/v59/i10/p952_s1",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}
@Article{Chen:1991:ZLN,
author = "Ye-Sho Chen",
title = "{Zipf}'s law in natural languages, programming
languages, and command languages: the {Simon--Yule}
approach",
journal = j-INT-J-SYST-SCI,
volume = "22",
number = "11",
pages = "2299--2312",
year = "1991",
CODEN = "IJSYA9",
DOI = "http://dx.doi.org/10.1080/00207729108910791",
ISSN = "0020-7721",
ISSN-L = "0020-7721",
bibdate = "Sat Nov 12 10:50:55 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0793.68020",
abstract = "Zipf's law and issues in natural languages,
programming languages and command languages related to
it, are reviewed. We point out the need for a unified
theory to resolve the issues. Based on Herbert Simon's
creative process for scientific discovery, we evaluate
four leading theories of language generation. As a
result, the Simon--Yule model of text generation is
selected as a promising theory. The implications of the
theory related to the issues in natural languages,
programming languages and command languages are
discussed.",
acknowledgement = ack-nhfb,
classmath = "68N15 (Programming languages) 68T50 (Natural language
processing)",
fjournal = "International Journal of Systems Science",
keywords = "command languages; natural languages; programming
languages; Simon-Yule model; text generation; Zipf's
law",
}
@Book{Durrett:1991:PTE,
author = "Richard Durrett",
title = "Probability: theory and examples",
publisher = "Wadsworth and Brooks\slash Cole Advanced Books and
Software",
address = "Pacific Grove, CA, USA",
pages = "ix + 453",
year = "1991",
ISBN = "0-534-13206-5",
ISBN-13 = "978-0-534-13206-4",
LCCN = "QA273 .D865 1991",
bibdate = "Mon Nov 21 10:06:18 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$49.95",
series = "The Wadsworth and Brooks\slash Cole statistics\slash
probability series",
acknowledgement = ack-nhfb,
remark = "Benford's Law is treated on pp. 300ff. Hill \cite[page
893]{Hill:1995:BII} reports that Durrett has a proof
that the $k$-th digit of powers of integers follows
Benford's Law.",
subject = "Probabilities",
}
@Book{Hardy:1991:DS,
author = "G. H. (Godfrey Harold) Hardy",
title = "Divergent series",
publisher = "Chelsea Pub. Co.",
address = "New York, NY, USA",
edition = "Second",
pages = "xvi + 396",
year = "1991",
ISBN = "0-8284-0334-1",
ISBN-13 = "978-0-8284-0334-4",
LCCN = "QA295 .H29 1991",
bibdate = "Wed Nov 16 08:17:27 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1877--1947",
remark = "Unaltered reprint of \cite{Hardy:1949:DS}, despite
label of second edition.",
subject = "Divergent series",
}
@Article{Katsikas:1991:CDG,
author = "A. A. Katsikas and J. S. Nicolis",
title = "Chaotic Dynamics of Generating {Markov} Partitions,
and Linguistic Sequences Mimicking {Zipf}'s Law",
journal = j-LECT-NOTES-COMP-SCI,
volume = "565",
pages = "335--??",
year = "1991",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon May 13 08:51:55 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Schatte:1991:NBL,
author = "P. Schatte and K. Nagasaka",
title = "A note on {Benford}'s law for second order linear
recurrences with periodical coefficients",
journal = j-Z-ANAL-ANWEND,
volume = "10",
number = "2",
pages = "251--254",
year = "1991",
CODEN = "????",
ISSN = "0232-2064",
ISSN-L = "0232-2064",
MRclass = "11K31",
MRnumber = "1155374 (93b:11101)",
MRreviewer = "F. Schweiger",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Analysis und ihre Anwendungen}",
}
@Article{Schatte:1991:ULI,
author = "P. Schatte",
title = "On a uniform law of the iterated logarithm for sums
mod {$1$} and {Benford}'s law",
journal = "Litovsk. Mat. Sb.",
volume = "31",
number = "1",
pages = "205--217",
year = "1991",
CODEN = "????",
DOI = "http://dx.doi.org/10.1007/BF00972327",
ISSN = "0132-2818",
ISSN-L = "0132-2818",
MRclass = "60F15 (11K99)",
MRnumber = "1161363 (93g:60067)",
MRreviewer = "O. P. Stackelberg",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Lietuvos TSR Moksl\polhk u Akademija. Lietuvos TSR
Auk\v stosios Mokyklos. Lietuvos Matematikos Rinkinys.
Akademiya Nauk Litovsko{\u\i} SSR. Vysshie Uchebnye
Zavedeniya Litovsko{\u\i} SSR. Litovski\u\i\
Matematicheski{\u\i} Sbornik",
xxnote = "Check pages: reprinted in two version of this
journal??",
}
@Article{Trubnikov:1991:SDZ,
author = "B. A. Trubnikov and I. A. Rumynski{\u\i}",
title = "A simple derivation of the {Zipf--Krylov} law for
words and the possibility of its ``evolution''
interpretation",
journal = j-DOKL-AKAD-NAUK,
volume = "321",
number = "2",
pages = "270--275",
year = "1991",
CODEN = "DANKAS",
ISSN = "0002-3264",
ISSN-L = "0002-3264",
MRclass = "00A69 (92K20)",
MRnumber = "1153554",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Doklady Akademii Nauk SSSR",
}
@TechReport{Busta:1992:TRN,
author = "B. Busta and R. Sundheim",
title = "Tax return numbers tend to obey {Benford}'s law",
type = "Working Paper",
number = "W93-106-94",
institution = "Center for Business Research, St. Cloud State
University",
address = "St. Cloud, MN, USA",
year = "1992",
bibdate = "Sat Feb 16 17:29:47 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Dehaene:1992:CLR,
author = "Stanislas Dehaene and Jacques Mehler",
title = "Cross-linguistic regularities in the frequency of
number words",
journal = j-COGNITION,
volume = "43",
number = "1",
pages = "1--29",
year = "1992",
CODEN = "CGTNAU",
DOI = "http://dx.doi.org/10.1016/0010-0277(92)90030-L",
ISSN = "0010-0277",
ISSN-L = "0010-0277",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/001002779290030L",
abstract = "We examine the frequency of numerals and ordinals in
seven different languages and/or cultures. Many
cross-cultural and cross-linguistic patterns are
identified. The most striking is a decrease of
frequency with numerical magnitude, with local
increases for reference numerals such as 10, 12, 15,
20, 50 or 100. Four explanations are considered for
this effect: sampling artifacts, notational
regularities, environmental biases and psychological
limitations on number representations. The
psychological explanation, which appeals to a
Fechnerian encoding of numerical magnitudes and to the
existence of numerical points of reference, accounts
for most of the data. Our finding also has practical
importance since it reveals the frequent confound of
two experimental variables: numerical magnitude and
numeral frequency.",
acknowledgement = ack-nhfb,
fjournal = "Cognition",
keywords = "Benford's Law",
}
@Article{Goto:1992:SEB,
author = "Kazuo Got{\^o}",
title = "Some examples of {Benford} sequences",
journal = "Math. J. Okayama Univ.",
volume = "34",
pages = "225--232 (1994)",
year = "1992",
CODEN = "MJOKAP",
ISSN = "0030-1566",
ISSN-L = "0030-1566",
MRclass = "11K36",
MRnumber = "1272624 (95c:11097)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Journal of Okayama University",
}
@Article{Gunther:1992:PCZ,
author = "R. G{\"u}nther and B. Schapiro and P. Wagner",
title = "Physical complexity and {Zipf}'s law",
journal = j-INT-J-THEOR-PHYS,
volume = "31",
number = "3",
pages = "525--543",
year = "1992",
CODEN = "IJTPBM",
DOI = "http://dx.doi.org/10.1007/BF00740003",
ISSN = "0020-7748 (print), 1572-9575 (electronic)",
ISSN-L = "0020-7748",
MRclass = "58F40",
MRnumber = "1154668 (92k:58252)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Theoretical Physics",
journal-URL = "http://link.springer.com/journal/10773",
}
@Article{Jech:1992:LDL,
author = "Thomas Jech",
title = "The logarithmic distribution of leading digits and
finitely additive measures",
journal = j-DISCRETE-MATH,
volume = "108",
number = "1--3",
pages = "53--57",
month = "????",
year = "1992",
CODEN = "DSMHA4",
ISSN = "0012-365X (print), 1872-681X (electronic)",
ISSN-L = "0012-365X",
bibdate = "Fri Nov 18 12:12:57 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete Mathematics",
}
@Article{Lagarias:1992:PTS,
author = "J. C. Lagarias and A. Weiss",
title = "The $ 3 x + 1 $ Problem: Two Stochastic Models",
journal = j-ANN-APPL-PROBAB,
volume = "2",
number = "1",
pages = "229--261",
month = feb,
year = "1992",
CODEN = "????",
ISSN = "1050-5164",
ISSN-L = "1050-5164",
bibdate = "Fri Jun 6 11:35:34 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/annapplprobab.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/euclid.aoap/1177005779",
acknowledgement = ack-nhfb,
fjournal = "Annals of Applied Probability",
journal-URL = "http://projecteuclid.org/all/euclid.aoap/;
http://www.jstor.org/journals/10505164.html;",
}
@Article{Li:1992:RTE,
author = "W. Li",
title = "Random texts exhibit {Zipf}'s-law-like word frequency
distribution",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "38",
number = "6",
pages = "1842--1845",
month = "????",
year = "1992",
CODEN = "IETTAW",
DOI = "http://dx.doi.org/10.1109/18.165464",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Fri Nov 18 12:32:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}
@PhdThesis{Nigrini:1992:DIE,
author = "Mark John Nigrini",
title = "The detection of income tax evasion through an
analysis of digital distributions",
type = "{Ph.D.} Dissertation",
school = "Department of Accounting\slash Business Law,
University of Cincinnati",
address = "Cincinnati, OH, USA",
pages = "xvi + 309",
day = "28",
month = aug,
year = "1992",
bibdate = "Sat Nov 12 15:47:41 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://search.proquest.com/docview/304052348",
acknowledgement = ack-nhfb,
advisor = "Wallace R. Wood",
remark = "There are more than 230 mentions of Frank Benford, and
8 of Simon Newcomb, but no mention of Pareto or Zipf.",
}
@Article{Sanders:1992:PPU,
author = "Robert Sanders",
title = "The {Pareto Principle}: its Use and Abuse",
journal = j-J-PROD-BRAND-MANAG,
volume = "1",
number = "2",
pages = "37--40",
month = "????",
year = "1992",
CODEN = "????",
DOI = "http://dx.doi.org/10.1108/10610429210036762",
ISSN = "1061-0421",
ISSN-L = "1061-0421",
bibdate = "Fri Nov 25 06:50:32 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Product \& Brand Management",
keywords = "80/20 rule",
}
@Article{Too:1992:UDM,
author = "Yeu-Hua Too",
title = "On the uniform distribution modulo one of some
log-like sequences",
journal = "Proceedings of the Japan Academy, Series A.
Mathematical Sciences",
volume = "68",
number = "9",
pages = "269--272",
month = "????",
year = "1992",
DOI = "http://dx.doi.org/10.3792/pjaa.68.269",
ISSN = "0021-4280",
ISSN-L = "0021-4280",
bibdate = "Mon Feb 18 06:55:06 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/euclid.pja/1195511634",
acknowledgement = ack-nhfb,
}
@Article{Trachtenberg:1992:WFR,
author = "M. Trachtenberg",
title = "Why failure rates observe {Zipf}'s law in operational
software",
journal = j-IEEE-TRANS-RELIAB,
volume = "41",
number = "3",
pages = "386--389",
year = "1992",
CODEN = "IEERAJ",
DOI = "http://dx.doi.org/10.1109/24.159803",
ISSN = "0018-9529 (print), 1558-1721 (electronic)",
ISSN-L = "0018-9529",
bibdate = "Sat Nov 12 10:50:55 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0825.68222",
acknowledgement = ack-nhfb,
classmath = "68M15 (Reliability and testing of computer systems)
68N01 (General)",
fjournal = "IEEE Transactions on Reliability",
}
@Article{Anonymous:1993:WFR,
author = "Anonymous",
title = "Why failure rates observe {Zipf}'s law in operational
software: {M. Trachtenberg. IEEE Transactions on
Reliability, {\bf 41}(3), 386 (1992)}",
journal = j-MICROELECT-RELIABILITY,
volume = "33",
number = "13",
pages = "2062--2062",
month = oct,
year = "1993",
CODEN = "MCRLAS",
DOI = "http://dx.doi.org/10.1016/0026-2714(93)90406-O",
ISSN = "0026-2714 (print), 1872-941X (electronic)",
ISSN-L = "0026-2714",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/002627149390406O",
acknowledgement = ack-nhfb,
fjournal = "Microelectronics and Reliability",
keywords = "Zipf's Law",
}
@Article{Buck:1993:IBF,
author = "B. Buck and A. C. Merchant and S. M. Perez",
title = "An illustration of {Benford}'s first digit law using
alpha decay half lives",
journal = j-EUR-J-PHYS,
volume = "14",
number = "2",
pages = "59--63",
month = "????",
year = "1993",
CODEN = "EJPHD4",
ISSN = "0143-0807 (print), 1361-6404 (electronic)",
ISSN-L = "0143-0807",
bibdate = "Mon Nov 14 17:32:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/1993EJPh...14...59B",
acknowledgement = ack-nhfb,
fjournal = "European Journal of Physics",
journal-URL = "http://iopscience.iop.org/0143-0807/",
}
@Article{Deakin:1993:ADB,
author = "Michael A. B. Deakin",
title = "Another derivation of {Benford}'s law",
journal = j-AUSTRALIAN-MATH-SOC-GAZ,
volume = "20",
number = "5",
pages = "162--163",
year = "1993",
CODEN = "????",
ISSN = "0311-0729",
ISSN-L = "0311-0729",
MRclass = "11K36",
MRnumber = "1268513 (95j:11072)",
MRreviewer = "Jean-Loup Mauclaire",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Australian Mathematical Society Gazette",
}
@Article{Nigrini:1993:CBL,
author = "Mark Nigrini",
title = "Can {Benford's Law} be used in Forensic Accounting?",
journal = "The Balance Sheet",
volume = "??",
number = "??",
pages = "7--8",
month = jun,
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 21 22:03:06 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Stewart:1993:LAN,
author = "Ian Stewart",
title = "The law of anomalous numbers",
type = "Working paper",
institution = "Mathematics Institute, University of Warwick",
address = "Warwick, UK",
year = "1993",
bibdate = "Fri Mar 22 09:15:03 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Published in Spektrum der Wissenschaft (April 1994)",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
}
@TechReport{Sundheim:1993:FNT,
author = "R. Sundheim and B. Busta",
title = "{Fibonacci} numbers tend to obey {Benford's Law}: an
extension of {Wlodarski} and {Sentance}",
type = "Working Paper",
institution = "St. Cloud State University",
address = "St. Cloud, MN, USA",
month = "????",
year = "1993",
bibdate = "Mon Feb 18 06:37:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Sury:1993:FPD,
author = "B. Sury",
title = "Fractional parts of $ \log p $ and a digit function",
journal = j-EXPO-MATH,
volume = "11",
number = "4",
pages = "381--384",
month = "????",
year = "1993",
DOI = "????",
ISSN = "0723-0869 (print), 1878-0792 (electronic)",
ISSN-L = "0723-0869",
bibdate = "Mon Feb 18 06:39:02 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "????",
ZMnumber = "0787.11003",
acknowledgement = ack-nhfb,
ajournal = "Expo. Math.",
fjournal = "Expositiones Mathematicae",
journal-URL = "http://www.sciencedirect.com/science/journal/07230869",
keywords = "decimal expansion; sum of digits",
ZMclass = "11A63 (Radix representation; digital problems)",
ZMreviewer = "G. Larcher (Salzburg)",
}
@Article{Wolf:1993:PHJ,
author = "Joel L. Wolf and Philip S. Yu and John Turek and
Daniel M. Dias",
title = "A parallel hash join algorithm for managing data
skew",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "4",
number = "12",
pages = "1355--1371",
month = dec,
year = "1993",
CODEN = "ITDSEO",
DOI = "http://dx.doi.org/10.1109/71.250117",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Fri Apr 11 15:20:39 MDT 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
acknowledgement = ack-nhfb,
affiliation = "IBM T. J. Watson Research Cent",
affiliationaddress = "Yorktown Heights, NY, USA",
classification = "721.1; 722.4; 723.1; 723.2; 723.3; 921.4; C4240P
(Parallel programming and algorithm theory); C4250
(Database theory); C6160D (Relational DBMS)",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "http://www.computer.org/portal/web/csdl/transactions/tpds",
journalabr = "IEEE Trans Parallel Distrib Syst",
keywords = "Algorithms; combinatorial; Combinatorial mathematics;
Combinatorial optimization; Complex queries; complex
queries; Computational complexity; Data handling; Data
skew; data skew; database theory; hash; Hash joins;
hashing; heuristic optimization; hierarchical; join
column; joins; load balancing; Load balancing;
optimization; parallel algorithms; parallel hash join
algorithm; Parallel processing systems; Program
processors; Query languages; query processing;
Relational database systems; relational databases;
resource allocation; scheduling; Zipf-like
distribution",
treatment = "T Theoretical or Mathematical",
}
@Article{Wolf:1993:PSM,
author = "Joel L. Wolf and Daniel M. Dias and Philip S. Yu",
title = "Parallel sort merge join algorithm for managing data
skew",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "4",
number = "1",
pages = "70--86",
month = jan,
year = "1993",
CODEN = "ITDSEO",
DOI = "http://dx.doi.org/10.1109/71.205654",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Fri Apr 11 15:20:39 MDT 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
acknowledgement = ack-nhfb,
affiliation = "IBM",
affiliationaddress = "Yorktown Heights, NY, USA",
classification = "723.1; 723.3; 921.5; C4240P (Parallel programming
and algorithm theory); C4250 (Database theory); C6130
(Data handling techniques); C6160B (Distributed DBMS);
C6160D (Relational DBMS)",
corpsource = "IBM T. J. Watson Res. Center. Yorktown Heights, NY,
USA",
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "http://www.computer.org/portal/web/csdl/transactions/tpds",
journalabr = "IEEE Trans Parallel Distrib Syst",
keywords = "Algorithms; Computer systems programming; Data skew;
data skew management; distributed databases; Divide and
conquer approach; divide-and-conquer; join phases; load
balancing; merging; multiple processors;
Multiprocessing programs; Optimization; parallel;
Parallel algorithms; parallel algorithms; Parallel sort
merge join algorithm; parallelizable optimization
algorithm; phase; Query processing; relational algebra;
Relational database systems; relational databases;
scheduling; Scheduling; sort merge join algorithm; sort
phase; sorting; Sorting; transfer phase; Zipf-like
distribution",
treatment = "T Theoretical or Mathematical",
}
@Book{Arthur:1994:IRP,
author = "W. Brian Arthur",
title = "Increasing returns and path dependence in the
economy",
publisher = pub-U-MICHIGAN,
address = pub-U-MICHIGAN:adr,
pages = "xx + 201",
year = "1994",
ISBN = "0-472-09496-3 , 0-472-06496-7 (paperback)",
ISBN-13 = "978-0-472-09496-7, 978-0-472-06496-0 (paperback)",
LCCN = "HD69.S5 A77 1994",
bibdate = "Wed Feb 27 07:08:40 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
note = "With a foreword by Kenneth J. Arrow.",
series = "Economics, cognition, and society",
acknowledgement = ack-nhfb,
keywords = "Zipf's Law",
subject = "Economies of scale; Mathematical models; Economic
development; Economics, Mathematical",
}
@Article{Boyle:1994:AFS,
author = "Jeff Boyle",
title = "An application of {Fourier} series to the most
significant digit problem",
journal = j-AMER-MATH-MONTHLY,
volume = "101",
number = "9",
pages = "879--886",
month = nov,
year = "1994",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "60F99",
MRnumber = "1 300 493",
bibdate = "Wed Dec 3 17:17:33 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Article{Fuchs:1994:PDP,
author = "Aim{\'e} Fuchs and Giorgio Letta",
title = "Le probl{\`e}me du premier chiffre d{\'e}cimal pour
les nombres premiers. ({French}) [The problem for the
first decimal digit of prime numbers]",
journal = "Rendiconti della Accademia Nazionale delle Scienze
detta dei XL. Serie V. Memorie di Matem{\`a}tica",
volume = "18",
number = "1",
pages = "81--87",
month = "????",
year = "1994",
bibdate = "Sat Feb 16 17:40:01 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf",
ZMnumber = "0838.11004",
acknowledgement = ack-nhfb,
ajournal = "Rend. Accad. Naz. Sci. XL, V. Ser., Mem. Mat.",
keywords = "asymptotic densities; logarithmic density; primes;
relative densities",
language = "French",
xxjournal = "Rend. Acad. Naz. Sci. Detta",
xxvolume = "XL",
ZMclass = "11B05 (Topology etc. of sets of numbers); 11K16
(Normal numbers, etc.)",
ZMreviewer = "I. Z. Ruzsa (Budapest)",
}
@Article{Ley:1994:TPB,
author = "Eduadro Ley and Hal R. Varian",
title = "Are there psychological barriers in the {Dow--Jones}
index?",
journal = j-APPL-FINANC-ECON,
volume = "4",
number = "3",
pages = "217--224",
month = "????",
year = "1994",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/758526902",
ISSN = "0960-3107 (print), 1466-4305 (electronic)",
ISSN-L = "0960-3107",
bibdate = "Sat Feb 16 18:29:52 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/758526902",
acknowledgement = ack-nhfb,
fjournal = "Applied Financial Economics",
}
@Article{Mantegna:1994:LFN,
author = "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger
and S. Havlin and C. K. Peng and M. Simons and H. E.
Stanley",
title = "Linguistic Features of Noncoding {DNA} Sequences",
journal = j-PHYS-REV-LET,
volume = "73",
number = "??",
pages = "3169--??",
day = "5",
month = dec,
year = "1994",
CODEN = "PRLTAO",
DOI = "http://dx.doi.org/10.1103/PhysRevLett.73.3169",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.73.3169",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Nigrini:1994:UDF,
author = "Mark J. Nigrini",
title = "Using digital frequencies to detect fraud",
journal = "The White Paper",
volume = "??",
number = "??",
pages = "3--6",
month = apr # "\slash " # may,
year = "1994",
bibdate = "Sat Feb 16 18:53:08 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
remark = "The White Paper is the precursor to Fraud Magazine; I
cannot find it in the Library of Congress catalog.",
}
@Article{Pedrotti:1994:ALU,
author = "A. Pedrotti",
title = "Analysis of a list-update strategy",
journal = j-INFO-PROC-LETT,
volume = "52",
number = "3",
pages = "115--121",
day = "11",
month = nov,
year = "1994",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Wed Nov 11 12:16:26 MST 1998",
bibsource = "Compendex database;
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
affiliation = "Scuola Normale Superiore",
affiliationaddress = "Pisa, Italy",
classification = "721.1; 723.2; 921.6; 922.1; 922.2; C4240C
(Computational complexity); C6130 (Data handling
techniques)",
corpsource = "Scuola Normale Superiore, Pisa, Italy",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
journalabr = "Inf Process Lett",
keywords = "Algorithms; analysis of algorithms; average-case
complexity; BIT; competitive algorithms; Computational
complexity; computational complexity; convergence;
Convergence of numerical methods; Data handling;
Function evaluation; Heuristic methods; list
processing; list update; Markov chains; Move to front
algorithm; move-to-front; Probability; Random number
generation; searching; Theorem proving; transpose;
Zipf's law",
treatment = "T Theoretical or Mathematical",
}
@Article{Sheppard:1994:TNA,
author = "Lee A. Sheppard",
title = "{Tax Notes} audits the {Clintons}",
journal = "Tax Notes Today",
volume = "??",
number = "??",
pages = "18--23",
day = "4",
month = apr,
year = "1994",
bibdate = "Fri Mar 22 09:13:48 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.bankler.com/docs/Tax_Notes_Audits_the_Clintons.pdf",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
}
@Article{Tritch:1994:MAC,
author = "Teresa Tritch and Mary L. Sprouse",
title = "{Money} audits the {Clintons}",
journal = "Money Magazine",
volume = "??",
number = "??",
pages = "84--98",
day = "1",
month = apr,
year = "1994",
bibdate = "Fri Mar 22 09:16:28 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://money.cnn.com/magazines/moneymag/moneymag_archive/1994/04/01/88775/index.htm",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
}
@Article{Berton:1995:HGT,
author = "L. Berton",
title = "He's Got their Number. {Scholar} Uses Math to Foil
Financial Fraud",
journal = j-WALL-ST-J,
volume = "??",
number = "??",
pages = "??--??",
day = "10",
month = jul,
year = "1995",
CODEN = "WSJOAF",
ISSN = "0099-9660",
ISSN-L = "0099-9660",
bibdate = "Sat Dec 10 11:17:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Wall Street Journal",
}
@Book{Bologna:1995:FAF,
author = "Jack Bologna and Robert J. Lindquist",
title = "Fraud auditing and forensic accounting: new tools and
techniques",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Second",
pages = "xv + 249",
year = "1995",
ISBN = "0-471-10646-1 (hardcover)",
ISBN-13 = "978-0-471-10646-3 (hardcover)",
LCCN = "HV8079.W47 B65 1995",
bibdate = "Tue Nov 22 10:31:53 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/bios/wiley042/95005510.html;
http://www.loc.gov/catdir/description/wiley033/95005510.html;
http://www.loc.gov/catdir/toc/onix04/95005510.html",
acknowledgement = ack-nhfb,
remark = "This book does not discuss Benford's Law, but may be
helpful background for application of that law to the
detection of fraud.",
subject = "white collar crime investigation; United States;
forensic accounting; fraud investigation",
}
@Article{Czirok:1995:CBS,
author = "Andras Czir{\'o}k and Rosario N. Mantegna and Shlomo
Havlin and H. Eugene Stanley",
title = "Correlations in binary sequences and a generalized
{Zipf} analysis",
journal = j-PHYS-REV-E,
volume = "52",
number = "??",
pages = "446--??",
day = "1",
month = jul,
year = "1995",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.52.446",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.52.446",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Filipponi:1995:SPA,
author = "Piero Filipponi and Renato Menicocci",
title = "Some Probabilistic Aspects of the Terminal Digits of
{Fibonacci} Numbers",
journal = j-FIB-QUART,
volume = "33",
number = "4",
pages = "325--331",
month = aug,
year = "1995",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:02:19 MDT 2011",
bibsource = "http://www.fq.math.ca/33-4.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/33-4/filipponi.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Havlin:1995:DBZ,
author = "Shlomo Havlin",
title = "The distance between {Zipf} plots",
journal = j-PHYSICA-A,
volume = "216",
number = "1--2",
pages = "148--150",
day = "1",
month = jun,
year = "1995",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/0378-4371(95)00069-J",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037843719500069J",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Article{Hill:1995:BII,
author = "Theodore P. Hill",
title = "Base-invariance implies {Benford's Law}",
journal = j-PROC-AM-MATH-SOC,
volume = "123",
number = "3",
pages = "887--895",
month = mar,
year = "1995",
CODEN = "PAMYAR",
DOI = "http://dx.doi.org/10.2307/2160815",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "60A10 (28D05)",
MRnumber = "1233974 (95d:60006)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2160815",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
}
@Article{Hill:1995:SDP,
author = "Theodore P. Hill",
title = "The significant-digit phenomenon",
journal = j-AMER-MATH-MONTHLY,
volume = "102",
number = "4",
pages = "322--327",
month = apr,
year = "1995",
CODEN = "AMMYAE",
DOI = "http://dx.doi.org/10.2307/2974952",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11K99 (60E99)",
MRnumber = "96f:11101",
MRreviewer = "Jean-Loup Mauclaire",
bibdate = "Wed Dec 3 17:17:33 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Article{Hill:1995:SDS,
author = "Theodore P. Hill",
title = "A statistical derivation of the significant-digit
law",
journal = j-STAT-SCI,
volume = "10",
number = "4",
pages = "354--363",
year = "1995",
CODEN = "STSCEP",
ISSN = "0883-4237",
ISSN-L = "0883-4237",
MRclass = "60E99 (60A10 62E99)",
MRnumber = "1421567 (98a:60021)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 10:09:36 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "2-P&origin=MSN;
http://links.jstor.org/sici?sici=0883-4237(199511)10:4<354:ASDOTS>2.0.CO",
ZMnumber = "Zbl 0955.60509",
acknowledgement = ack-nhfb,
fjournal = "Statistical Science. A Review Journal of the Institute
of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.ss",
}
@Article{Kanter:1995:MPL,
author = "I. Kanter and D. A. Kessler",
title = "{Markov} Processes: Linguistics and {Zipf's Law}",
journal = j-PHYS-REV-LET,
volume = "74",
number = "??",
pages = "4559--??",
day = "29",
month = may,
year = "1995",
CODEN = "PRLTAO",
DOI = "http://dx.doi.org/10.1103/PhysRevLett.74.4559",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.74.4559",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Makse:1995:MUG,
author = "Hern{\'a}n A. Makse and Shlomo Havlin and H. Eugene
Stanley",
title = "Modelling urban growth patterns",
journal = j-NATURE,
volume = "377",
number = "6550",
pages = "608--612",
day = "19",
month = oct,
year = "1995",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/377608a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Feb 27 06:06:25 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.nature.com/nature/journal/v377/n6550/abs/377608a0.html",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Berlin (Germany) population; London (UK) population;
Zipf's Law",
}
@Article{Mantegna:1995:SAC,
author = "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger
and S. Havlin and C.-K. Peng and M. Simons and H. E.
Stanley",
title = "Systematic analysis of coding and noncoding {DNA}
sequences using methods of statistical linguistics",
journal = j-PHYS-REV-E,
volume = "52",
number = "??",
pages = "2939--??",
day = "1",
month = sep,
year = "1995",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.52.2939",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.52.2939",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Mosimann:1995:DFC,
author = "James E. Mosimann and Claire V. Wiseman and Ruth E.
Edelman",
title = "Data Fabrication: Can People Generate Random Digits?",
journal = j-ACCOUNT-RES,
volume = "4",
number = "1",
pages = "31--55",
month = "????",
year = "1995",
CODEN = "ARQAEZ",
ISSN = "0898-9621 (print), 1545-5815 (electronic)",
ISSN-L = "0898-9621",
bibdate = "Sat Dec 10 11:56:38 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/08989629508573866",
acknowledgement = ack-nhfb,
fjournal = "Accountability in Research",
keywords = "Benford's Law",
remark = "The abstract ends with: ``The difficulty that people
have in creating random error digits supports the
utility of examining such digits in investigations of
scientific misconduct.''",
}
@Article{Stanley:1995:ZPS,
author = "Michael H. R. Stanley and Sergey V. Buldyrev and
Shlomo Havlin and Rosario N. Mantegna and Michael A.
Salinger and H. Eugene Stanley",
title = "{Zipf} plots and the size distribution of firms",
journal = j-ECONOM-LETT,
volume = "49",
number = "4",
pages = "453--457",
day = "15",
month = oct,
year = "1995",
CODEN = "ECLEDS",
DOI = "http://dx.doi.org/10.1016/0165-1765(95)00696-D",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/016517659500696D",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
keywords = "Zipf's Law",
}
@Article{Wagner-Dobler:1995:DLL,
author = "Roland Wagner-D{\"o}bler and Jan Berg",
title = "The Dependence of {Lotka's Law} on the Selection of
Time Periods in the Development of Scientific Areas and
Authors",
journal = j-J-DOC,
volume = "51",
number = "1",
pages = "28--43",
month = "????",
year = "1995",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/eb026941",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:29:22 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@Article{Zornig:1995:URZ,
author = "Peter Z{\"o}rnig and Gabriel Altmann",
title = "Unified representation of {Zipf} distributions",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "19",
number = "4",
pages = "461--473",
day = "1",
month = apr,
year = "1995",
CODEN = "CSDADW",
DOI = "http://dx.doi.org/10.1016/0167-9473(94)00009-8",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
MRclass = "62E10 (62F10)",
MRnumber = "1333065 (96f:62029)",
MRreviewer = "Friedrich Liese",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0167947394000098",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
keywords = "Zipf's Law",
}
@Book{Bak:1996:HNW,
author = "Per Bak",
title = "How nature works: the science of self-organized
criticality",
publisher = "Copernicus",
address = "New York, NY, USA",
pages = "xiii + 212 + 8",
year = "1996",
ISBN = "0-387-94791-4 (hardcover)",
ISBN-13 = "978-0-387-94791-4 (hardcover)",
LCCN = "QC173.4.C74 B34 1996",
bibdate = "Thu Nov 24 13:34:22 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
keywords = "Zipf's Law",
subject = "Critical phenomena (Physics); Complexity (Philosophy);
Physics; Philosophy",
}
@Article{Beirlant:1996:TIE,
author = "Jan Beirlant and Petra Vynckier and Jozef L. Teugels",
title = "Tail Index Estimation, {Pareto} Quantile Plots, and
Regression Diagnostics",
journal = j-J-AM-STAT-ASSOC,
volume = "91",
number = "436",
pages = "1659--??",
month = "????",
year = "1996",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Mon May 5 08:26:17 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Burgos:1996:ZSB,
author = "Javier D. Burgos and Pedro Moreno-Tovar",
title = "{Zipf}-scaling behavior in the immune system",
journal = j-BIOSYSTEMS,
volume = "39",
number = "3",
pages = "227--232",
day = "15",
month = nov,
year = "1996",
CODEN = "BSYMBO",
DOI = "http://dx.doi.org/10.1016/0303-2647(96)01618-8",
ISSN = "0303-2647 (print), 1872-8324 (electronic)",
ISSN-L = "0303-2647",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0303264796016188",
acknowledgement = ack-nhfb,
fjournal = "Biosystems (A6E)",
keywords = "Zipf's Law",
}
@Article{Campanino:1996:IIM,
author = "Massimo Campanino and Stefano Isola",
title = "Infinite invariant measures for non-uniformly
expanding transformations of $ [0, 1] $: Weak law of
large numbers with anomalous scaling",
journal = j-FORUM-MATH,
volume = "8",
number = "1",
pages = "71--92",
year = "1996",
CODEN = "FOMAEF",
DOI = "http://dx.doi.org/10.1515/form.1996.8.71",
ISSN = "0933-7741 (print), 1435-5337 (electronic)",
ISSN-L = "0933-7741",
bibdate = "Sat Nov 12 10:33:06 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0837.60022",
abstract = "We consider a class of maps of $ [0, 1] $ with an
indifferent fixed point at 0 and expanding everywhere
else. Using the invariant ergodic probability measure
of a suitable, everywhere expanding, induced
transformation we are able to study the infinite
invariant measure of the original map in some detail.
Given a continuous function with compact support in
$]0, 1]$, we prove that its time averages satisfy a
`weak law of large numbers' with anomalous scaling $ n
/ \log n $ and give an upper bound for the decay of
correlations.",
acknowledgement = ack-nhfb,
ajournal = "Forum Math.",
classmath = "60F05 (Weak limit theorems) 28D05 (Measure-preserving
transformations) 37A99 (Ergodic theory)",
fjournal = "Forum Mathematicum",
keywords = "decay of correlations; invariant ergodic probability
measure; weak law of large numbers",
}
@Article{Czirok:1996:POP,
author = "Andr{\'a}s Czir{\'o}k and H. Eugene Stanley and
Tam{\'a}s Vicsek",
title = "Possible origin of power-law behavior in $n$-tuple
{Zipf} analysis",
journal = j-PHYS-REV-E,
volume = "53",
number = "??",
pages = "6371--??",
day = "1",
month = jun,
year = "1996",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.53.6371",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.53.6371",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Fuchs:1996:PDP,
author = "Aim{\'e} Fuchs and Giorgio Letta",
title = "Le probl{\`e}me du premier chiffre d{\'e}cimal pour
les nombres premiers. ({French}) [The problem for the
first decimal digit of prime numbers]",
journal = j-ELECT-J-COMB,
volume = "3",
number = "2",
pages = "R25:1--R25:7",
month = "????",
year = "1996",
ISSN = "1077-8926 (print), 1097-1440 (electronic)",
ISSN-L = "1077-8926",
bibdate = "Sat Feb 16 17:40:01 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "The Foata Festschrift volume.",
URL = "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf",
ZMnumber = "0853.11006",
acknowledgement = ack-nhfb,
fjournal = "Electronic Journal of Combinatorics",
language = "French",
xxpages = "601--607",
}
@Article{Gunther:1996:ZLE,
author = "R. G{\"u}nther and L. Levitin and B. Schapiro and P.
Wagner",
title = "{Zipf}'s law and the effect of ranking on probability
distributions",
journal = j-INT-J-THEOR-PHYS,
volume = "35",
number = "2",
pages = "395--417",
year = "1996",
CODEN = "IJTPBM",
DOI = "http://dx.doi.org/10.1007/BF02083823",
ISSN = "0020-7748 (print), 1572-9575 (electronic)",
ISSN-L = "0020-7748",
bibdate = "Sat Nov 12 10:53:57 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0843.60002",
abstract = "Ranking procedures are widely used in the description
of many different types of complex systems. Zipf's law
is one of the most remarkable frequency-rank
relationships and has been observed independently in
physics, linguistics, biology, demography, etc. We show
that ranking plays a crucial role in making it possible
to detect empirical relationships in systems that exist
in one realization only, even when the statistical
ensemble to which the systems belong has a very broad
probability distribution. Analytical results and
numerical simulations are presented which clarify the
relations between the probability distributions and the
behavior of expected values for unranked and ranked
random variables. This analysis is performed, in
particular, for the evolutionary model presented in our
previous papers which leads to Zipf's law and reveals
the underlying mechanism of this phenomenon in terms of
a system with interdependent and interacting components
as opposed to the ``ideal gas'' models suggested by
previous researchers. The ranking procedure applied to
this model leads to a new, unexpected phenomenon: a
characteristic ``staircase'' behavior of the mean
values of the ranked variables (ranked occupation
numbers). This result is due to the broadness of the
probability distributions for the occupation numbers
and does not follow from the ``ideal gas'' model. Thus,
it provides an opportunity, by comparison with
empirical data, to obtain evidence as to which model
relates to reality.",
acknowledgement = ack-nhfb,
classmath = "60A99 (Foundations of probability theory)",
fjournal = "International Journal of Theoretical Physics",
journal-URL = "http://link.springer.com/journal/10773",
keywords = "numerical simulations; ranking procedures; Zipf's
law",
}
@TechReport{Hill:1996:NDT,
author = "Theodore P. Hill",
title = "A note on distributions of true versus fabricated
data",
type = "Preprint",
institution = "Department of Mathematics, Georgia Institute of
Technology",
address = "Atlanta, GA, USA",
pages = "4",
year = "1996",
bibdate = "Sat Feb 16 17:47:27 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1046&context=rgp_rsr",
acknowledgement = ack-nhfb,
}
@Article{Israeloff:1996:CZD,
author = "N. E. Israeloff and M. Kagalenko and K. Chan",
title = "Can {Zipf} Distinguish Language From Noise in
Noncoding {DNA}?",
journal = j-PHYS-REV-LET,
volume = "76",
number = "??",
pages = "1976--??",
day = "11",
month = mar,
year = "1996",
CODEN = "PRLTAO",
DOI = "http://dx.doi.org/10.1103/PhysRevLett.76.1976",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.76.1976",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Krugman:1996:CMU,
author = "Paul Krugman",
title = "Confronting the Mystery of Urban Hierarchy",
journal = j-J-JPN-INT-ECON,
volume = "10",
number = "4",
pages = "399--418",
month = dec,
year = "1996",
CODEN = "JJIEBD",
DOI = "http://dx.doi.org/10.1006/jjie.1996.0023",
ISSN = "0889-1583 (print), 1095-8681 (electronic)",
ISSN-L = "0889-1583",
bibdate = "Wed Feb 27 06:15:55 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0889158396900234",
acknowledgement = ack-nhfb,
fjournal = "Journal of the {Japanese} and International
Economies",
keywords = "Zipf's Law",
}
@Book{Krugman:1996:SOE,
author = "Paul R. Krugman",
title = "The Self-Organizing Economy",
publisher = "Blackwell Publishers",
address = "Cambridge, MA, USA",
pages = "vi + 122",
year = "1996",
ISBN = "1-55786-699-6 (paperback)",
ISBN-13 = "978-1-55786-699-8 (paperback)",
LCCN = "HB199 .K75 1996",
bibdate = "Wed Feb 27 07:08:14 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
keywords = "Zipf's Law",
subject = "Economics; Self-organizing systems",
}
@Article{Ley:1996:PDU,
author = "Eduardo Ley",
title = "On the Peculiar Distribution of the {U.S.} Stock
Indexes' Digits",
journal = j-AMER-STAT,
volume = "50",
number = "4",
pages = "311--313",
month = nov,
year = "1996",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Mon Nov 14 15:09:04 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/2684926",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Newman:1996:ASC,
author = "M. E. J. Newman and Kim Sneppen",
title = "Avalanches, scaling, and coherent noise",
journal = j-PHYS-REV-E,
volume = "54",
number = "6",
pages = "6226--6231",
month = dec,
year = "1996",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.54.6226",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Thu Feb 28 10:44:51 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.54.6226",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Nigrini:1996:TCA,
author = "M. Nigrini",
title = "A Taxpayer Compliance Application of {Benford's Law}",
journal = "Journal of the American Taxation Association",
volume = "18",
number = "1",
pages = "72--91",
month = "????",
year = "1996",
CODEN = "????",
ISSN = "0198-9073 (print), 1558-8017 (electronic)",
ISSN-L = "0198-9073",
bibdate = "Mon Nov 14 16:30:42 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Amer. Tax. Assoc.",
fjournal = "Journal of the American Taxation Association",
}
@Article{Perline:1996:ZLC,
author = "Richard Perline",
title = "{Zipf}'s law, the {Central Limit Theorem}, and the
random division of the unit interval",
journal = j-PHYS-REV-E,
volume = "54",
number = "1",
pages = "220--223",
day = "1",
month = jul,
year = "1996",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.54.220",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.54.220",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Mandelbrot's monkey-at-the-typewriter model of Zipf's
inverse power law; Zipf's Law",
}
@Article{Sole:1996:ESO,
author = "Ricard V. Sol{\'e} and Susanna C. Manrubia",
title = "Extinction and self-organized criticality in a model
of large-scale evolution",
journal = j-PHYS-REV-E,
volume = "54",
number = "1",
pages = "R42--R45",
month = jul,
year = "1996",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.54.R42",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Thu Feb 28 10:32:32 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.54.R42",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Solomon:1996:SSE,
author = "Sorin Solomon and Moshe Levy",
title = "Spontaneous Scaling Emergence in Generic Stochastic
Systems",
journal = j-INT-J-MOD-PHYS-C,
volume = "7",
number = "5",
pages = "745--752",
month = oct,
year = "1996",
CODEN = "IJMPEO",
DOI = "http://dx.doi.org/10.1142/S0129183196000624",
ISSN = "0129-1831 (print), 1793-6586 (electronic)",
bibdate = "Thu Feb 28 10:20:02 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.worldscientific.com/doi/abs/10.1142/S0129183196000624",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Modern Physics C [Physics and
Computers]",
journal-URL = "http://www.worldscientific.com/loi/ijmpc",
}
@Article{Watanabe:1996:EZL,
author = "Makoto S. Watanabe",
title = "Erratum: {Zipf}'s law in percolation",
journal = j-PHYS-REV-E,
volume = "54",
number = "??",
pages = "4483--??",
day = "1",
month = oct,
year = "1996",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.54.4483",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite {Watanabe:1996:ZLP}.",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.54.4483",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Watanabe:1996:ZLP,
author = "Makoto S. Watanabe",
title = "{Zipf}'s law in percolation",
journal = j-PHYS-REV-E,
volume = "53",
number = "??",
pages = "4187--??",
day = "1",
month = apr,
year = "1996",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.53.4187",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See erratum \cite {Watanabe:1996:EZL}.",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.53.4187",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Allaart:1997:ISC,
author = "Pieter C. Allaart",
title = "An Invariant-Sum Characterization of {Benford's Law}",
journal = j-J-APPL-PROBAB,
volume = "34",
number = "1",
pages = "288--291",
month = mar,
year = "1997",
CODEN = "JPRBAM",
DOI = "http://dx.doi.org/10.2307/3215195",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
MRclass = "60E05",
MRnumber = "1429075 (98d:60029)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/3215195",
abstract = "The accountant Nigrini remarked that in tables of data
distributed according to Benford's law, the sum of all
elements with first digit $ d (d = 1, 2, \ldots, 9) $
is approximately constant. In this note, a mathematical
formulation of Nigrini's observation is given and it is
shown that Benford's law is the unique probability
distribution such that the expected sum of all elements
with first digits $ d_1, \ldots, d_k $ is constant for
every fixed $k$.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Probability",
journal-URL = "http://www.jstor.org/journals/00219002.html;
http://projecteuclid.org/euclid.jap/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Castillo:1997:FGP,
author = "Enrique Castillo and Ali S. Hadi",
title = "Fitting the Generalized {Pareto} Distribution to
Data",
journal = j-J-AM-STAT-ASSOC,
volume = "92",
number = "440",
pages = "1609--1620",
month = dec,
year = "1997",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Mon Oct 30 06:57:36 MST 2000",
bibsource = "http://www.amstat.org/publications/jasa/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
URL = "http://www.amstat.org/publications/jasa/abstracts_97/december/CASTILLO.HTM;
http://www.jstor.org/stable/2965432",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Chen:1997:NHS,
author = "Weishing Chen and Tai-Hsi Wu",
title = "A non-homogeneous software reliability model based on
{Zipf}'s law",
journal = "International Journal of Quality \& Reliability
Management",
volume = "14",
number = "4",
pages = "409--431",
month = "????",
year = "1997",
DOI = "http://dx.doi.org/10.1108/02656719710170666",
ISSN = "0265-671X (print), 1758-6682 (electronic)",
ISSN-L = "0265-671X",
bibdate = "Fri Nov 25 07:08:17 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Denisov:1997:FBS,
author = "S. Denisov",
title = "Fractal binary sequences: {Tsallis} thermodynamics and
the {Zipf} law",
journal = j-PHYS-LET-A,
volume = "235",
number = "5",
pages = "447--451",
day = "17",
month = nov,
year = "1997",
CODEN = "PYLAAG",
DOI = "http://dx.doi.org/10.1016/S0375-9601(97)00688-9",
ISSN = "0375-9601 (print), 1873-2429 (electronic)",
ISSN-L = "0375-9601",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0375960197006889",
acknowledgement = ack-nhfb,
fjournal = "Physics Letters A",
journal-URL = "http://www.sciencedirect.com/science/journal/03759601",
keywords = "Zipf's Law",
}
@InCollection{Gell-Mann:1997:ETZ,
author = "Murray Gell-Mann",
title = "Empirical Theory --- {Zipf}'s Law",
crossref = "Gell-Mann:1997:QJA",
pages = "92--97",
year = "1997",
bibdate = "Mon Sep 01 10:20:00 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Hill:1997:BL,
author = "Theodore Hill",
editor = "Michiel Hazewinkel",
booktitle = "Encyclopedia of Mathematics, Supplement {I}",
title = "{Benford's Law}",
volume = "1",
publisher = pub-SV,
address = pub-SV:adr,
pages = "102--103",
year = "1997",
ISBN = "90-481-4896-0",
ISBN-13 = "978-90-481-4896-7",
LCCN = "????",
bibdate = "Wed Nov 16 10:29:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Irmay:1997:RBZ,
author = "Shragga Irmay",
title = "The relationship between {Zipf}'s law and the
distribution of first digits",
journal = j-J-APPL-STAT,
volume = "24",
number = "4",
pages = "383--393",
day = "1",
month = aug,
year = "1997",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
MRclass = "62E15",
MRnumber = "1491308 (98h:62015)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.catchword.co.uk/titles/carfax/02664763/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
URL = "http://www.tandfonline.com/doi/abs/10.1080/02664769723594",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
keywords = "Benford's Law; Zipf's Law",
xxpages = "383--394",
}
@Article{Jeevanand:1997:BEB,
author = "E. S. Jeevanand",
title = "{Bayes} Estimation of {$ P(X_2 < X_1) $} for a
Bivariate {Pareto} Distribution",
journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN,
volume = "46",
number = "1",
pages = "93--99",
month = "????",
year = "1997",
CODEN = "????",
DOI = "http://dx.doi.org/10.2307/2988496",
ISSN = "0039-0526 (print), 1467-9884 (electronic)",
ISSN-L = "0039-0526",
bibdate = "Thu Jan 22 18:10:24 MST 2015",
bibsource = "http://www.jstor.org/stable/i349996;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-d-1990.bib",
URL = "http://www.jstor.org/stable/2988496",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series D
(The Statistician)",
journal-URL = "http://www.jstor.org/journals/00390526.html",
}
@Book{Knuth:1997:SA,
author = "Donald E. Knuth",
title = "Seminumerical Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Third",
pages = "xiii + 762",
year = "1997",
ISBN = "0-201-89684-2",
ISBN-13 = "978-0-201-89684-8",
LCCN = "QA76.6 .K64 1997",
bibdate = "Fri Jul 11 15:41:22 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "See section 4.2.4V, The Fraction Parts, pages
254--262, for a discussion of Benford's Law.",
price = "US\$52.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
}
@Manual{Nigrini:1997:DAT,
author = "Mark J. Nigrini",
title = "Digital Analysis Tests and Statistics",
organization = "The Nigrini Institute, Inc.",
address = "Allen, TX, USA",
month = "????",
year = "1997",
bibdate = "Sat Feb 16 18:55:18 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.nigrini.com/data_software/Program_Details_2009.docx",
acknowledgement = ack-nhfb,
}
@Article{Nigrini:1997:UBL,
author = "M. J. Nigrini and L. J. Mittermaier",
title = "The Use of {Benford's Law} as an Aid in Analytical
Procedures",
journal = j-AUDITING,
volume = "16",
number = "2",
pages = "52--67",
month = "????",
year = "1997",
CODEN = "????",
ISSN = "0278-0380 (print), 1558-7991 (electronic)",
ISSN-L = "0278-0380",
bibdate = "Sun Nov 13 11:37:48 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://aaapubs.org/loi/ajpt",
acknowledgement = ack-nhfb,
fjournal = "Auditing: A Journal of Practice \& Theory",
}
@Article{Salsburg:1997:DPB,
author = "David Salsburg",
title = "Digit Preferences in the {Bible}",
journal = j-CHANCE,
volume = "10",
number = "4",
pages = "46--48",
month = "????",
year = "1997",
CODEN = "CNDCE4",
DOI = "http://dx.doi.org/10.1080/09332480.1997.10542065",
ISSN = "0933-2480 (print), 1867-2280 (electronic)",
ISSN-L = "0933-2480",
bibdate = "Sat Feb 16 19:08:02 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://amstat.tandfonline.com/doi/full/10.1080/09332480.1997.10542065",
acknowledgement = ack-nhfb,
fjournal = "Chance: a magazine for people interested in the
analysis of data",
journal-URL = "http://chance.amstat.org/;
http://link.springer.com/journal/144;
http://www.tandfonline.com/loi/ucha20",
}
@Article{Tsonis:1997:ZLS,
author = "A. A. Tsonis and C. Schultz and P. A. Tsonis",
title = "{Zipf's Law} and the structure and evolution of
languages",
journal = j-COMPLEXITY,
volume = "2",
number = "5",
pages = "12--13",
year = "1997",
CODEN = "COMPFS",
DOI = "2-C;
http://dx.doi.org/10.1002/(SICI)1099-0526(199705/06)2:5<12::AID-CPLX3>3.0.CO",
ISSN = "1076-2787 (print), 1099-0526 (electronic)",
ISSN-L = "1076-2787",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Complexity",
}
@Article{Zanette:1997:RIU,
author = "Dami{\'a}n H. Zanette and Susanna C. Manrubia",
title = "Role of Intermittency in Urban Development: A Model of
Large-Scale City Formation",
journal = j-PHYS-REV-LET,
volume = "79",
number = "3",
pages = "523--526",
day = "3",
month = jul,
year = "1997",
CODEN = "PRLTAO",
DOI = "http://dx.doi.org/10.1103/PhysRevLett.79.523",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Thu Feb 28 10:40:44 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.79.523",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Bach:1998:EPM,
author = "Eric Bach",
title = "Efficient prediction of {Marsaglia--Zaman} random
number generators",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "44",
number = "3",
pages = "1253--1257",
year = "1998",
CODEN = "IETTAW",
DOI = "http://dx.doi.org/10.1109/18.669305",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
MRclass = "65C10",
MRnumber = "99b:65007",
bibdate = "Thu Dec 22 07:42:24 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
ZMnumber = "0915.65003",
abstract = "This paper presents two properties of the random
number generator by {\it G. Marsaglia} and {\it A.
Zaman} [Ann. Appl. Probab. 1, No. 3, 462-480 (1991; Zbl
0733.65005)]. First, it is shown that its successive
digits are digits of certain rational $b$-adic numbers.
Then, an efficient algorithm is derived to predict an
unknown pseudorandom sequence of this type. Two
examples of the prediction are given.",
acknowledgement = ack-nhfb,
classmath = "*65C10 Random number generation 11K45 Pseudo-random
numbers, etc.",
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
keywords = "$b$-adic number; algorithm; continued fraction;
pseudo-random number generator",
ZMreviewer = "K. Uosaki (Tottori)",
}
@Article{Browne:1998:FBL,
author = "Malcolm W. Browne",
title = "Following {Benford's Law}, or Looking Out for {No.
1}",
journal = j-NY-TIMES,
volume = "??",
number = "??",
pages = "F4--F4",
day = "4",
month = aug,
year = "1998",
CODEN = "NYTIAO",
ISSN = "0362-4331 (print), 1542-667X, 1553-8095",
ISSN-L = "0362-4331",
bibdate = "Sat Feb 16 14:29:48 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Science section.",
URL = "http://search.proquest.com/hnpnewyorktimes/docview/109868161/13C4AACC02923FE97A/1",
acknowledgement = ack-nhfb,
fjournal = "New York Times",
journal-URL = "http://www.nytimes.com/",
}
@Article{Busta:1998:UBL,
author = "Bruce Busta and Randy Weinberg",
title = "Using {Benford's Law} and Neural Networks as a Review
Procedure",
journal = "Managerial Auditing Journal",
volume = "13",
number = "6",
pages = "356--366",
month = "????",
year = "1998",
CODEN = "????",
DOI = "http://dx.doi.org/10.1108/02686909810222375",
ISSN = "0268-6902 (print), 1758-7735 (electronic)",
ISSN-L = "0268-6902",
bibdate = "Tue Nov 22 18:50:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{DeCeuster:1998:HPB,
author = "Marc J. K. {De Ceuster} and Geert Dhaene and Tom
Schatteman",
title = "On the hypothesis of psychological barriers in stock
markets and {Benford's Law}",
journal = j-J-EMPIR-FINANCE,
volume = "5",
number = "3",
pages = "263--279",
month = sep,
year = "1998",
CODEN = "JEFIEC",
DOI = "http://dx.doi.org/10.1016/S0927-5398(97)00024-8",
ISSN = "0927-5398 (print), 1879-1727 (electronic)",
ISSN-L = "0927-5398",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0927539897000248",
abstract = "We consider the hypothesis of psychological barriers
at round numbers of a stock index. This hypothesis is
often examined by testing the uniformity of the
distribution of the trailing digits in the stock index,
a rejection being interpreted as evidencing the
existence of psychological barriers. By virtue of
Benford's Law, we show that the uniform distribution is
not the right benchmark against which to test. As an
alternative we propose a test based on the cyclical
permutations of the actual returns. Applying this test
to the Dow Jones 30 Industrial Average, the Financial
Times Stock Exchange 100 and the Nikkei Stock Average
225, we find no convincing evidence of psychological
barriers, contrary to previous findings.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Empirical Finance",
keywords = "Benford's Law; Psychological barriers",
}
@Article{Herman:1998:TRI,
author = "Tom Herman",
title = "Tax report: An {IRS} blooper startles thousands of
taxpayers",
journal = j-WALL-ST-J,
volume = "??",
number = "??",
pages = "1--1",
day = "18",
month = feb,
year = "1998",
CODEN = "WSJOAF",
ISSN = "0099-9660",
bibdate = "Fri Mar 22 09:17:50 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://online.wsj.com/article/SB887753996209804500.html",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
fjournal = "Wall Street Journal",
keywords = "Benford's Law",
remark = "From the article: ``[a taxpayer] was expecting a \$513
tax refund. Instead, he recently received a letter from
the Internal Revenue Service informing him that he owes
the government \$300,000,007.57. \ldots{} about 3,000
other people around the nation got similar erroneous
notices, each showing a balance due of `three hundred
million dollars and change.'\,''",
}
@Article{Hill:1998:FDP,
author = "Theodore P. Hill",
title = "The First Digit Phenomenon",
journal = j-AM-SCI,
volume = "86",
number = "4",
pages = "358--363",
month = jul # "\slash " # aug,
year = "1998",
CODEN = "AMSCAC",
DOI = "http://dx.doi.org/10.1511/1998.4.358",
ISSN = "0003-0996 (print), 1545-2786 (electronic)",
ISSN-L = "0003-0996",
bibdate = "Sat Dec 10 11:54:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://people.math.gatech.edu/~hill/publications/PAPER%20PDFS/TheFirstDigitPhenomenonAmericanScientist1996.pdf;
http://www.math.gatech.edu/~hill/publications/cv.dir/1st-dig.pdf",
abstract = "A century ago, Simon Newcomb observed an unexpected
pattern in the first digits of logarithm tables: The
digit $1$ is significantly more likely to occur than
$2$, $2$ than $3$, and so on. More than a half-century
later, Frank Benford rediscovered the first-digit
phenomenon and found that it applied to many tables of
numerical data, including the stock market, census
statistics and accounting figures. New mathematical
insights establish the empirical law developed by
Newcomb and Benford as part of modern probability
theory, and recent applications include testing of
mathematical models, design of computers and detection
of fraud in accounting.",
acknowledgement = ack-nhfb,
fjournal = "American Scientist",
journal-URL = "http://www.americanscientist.org/issues/past.aspx",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Manrubia:1998:IMU,
author = "Susanna C. Manrubia and Dami{\'a}n H. Zanette",
title = "Intermittency model for urban development",
journal = j-PHYS-REV-E,
volume = "58",
number = "1",
pages = "295--302",
month = jul,
year = "1998",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.58.295",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Thu Feb 28 10:42:23 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.58.295",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Marsili:1998:IIL,
author = "Matteo Marsili and Yi-Cheng Zhang",
title = "Interacting Individuals Leading to {Zipf's Law}",
journal = j-PHYS-REV-LET,
volume = "80",
number = "??",
pages = "2741--??",
day = "23",
month = mar,
year = "1998",
CODEN = "PRLTAO",
DOI = "http://dx.doi.org/10.1103/PhysRevLett.80.2741",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.80.2741",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Nigrini:1998:DIB,
author = "Mark J. Nigrini",
title = "{Dow} Illustrates {Benford's Law}",
journal = j-NY-TIMES,
volume = "??",
number = "??",
pages = "F4--F4",
day = "4",
month = aug,
year = "1998",
CODEN = "NYTIAO",
ISSN = "0362-4331 (print), 1542-667X, 1553-8095",
ISSN-L = "0362-4331",
bibdate = "Sat Feb 16 15:46:43 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://search.proquest.com/hnpnewyorktimes/docview/109901848/13C4AB0BB5661D397CE/1",
acknowledgement = ack-nhfb,
fjournal = "New York Times",
journal-URL = "http://www.nytimes.com/",
}
@Article{NunesAmaral:1998:PLS,
author = "Lu{\'\is} A. {Nunes Amaral} and Sergey V. Buldyrev and
Shlomo Havlin and Michael A. Salinger and H. Eugene
Stanley",
title = "Power Law Scaling for a System of Interacting Units
with Complex Internal Structure",
journal = j-PHYS-REV-LET,
volume = "80",
number = "7",
pages = "1385--1388",
day = "16",
month = feb,
year = "1998",
CODEN = "PRLTAO",
DOI = "http://dx.doi.org/10.1103/PhysRevLett.80.1385",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Thu Feb 28 11:09:02 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.80.1385",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Pietronero:1998:UDN,
author = "L. Pietronero and E. Tosatti and V. Tosatti and A.
Vespignani",
title = "The Uneven Distribution of Numbers in Nature",
journal = "ArXiv e-prints",
pages = "9",
day = "27",
month = aug,
year = "1998",
bibdate = "Mon Nov 21 06:58:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/cond-mat/9808305",
abstract = "Suppose you look at today's stock prices and bet on
the value of the first digit. One could guess that a
fair bet should correspond to the frequency of $ 1 / 9
= 11.11 \% $ for each digit from 1 to 9. This is by no
means the case, and one can easily observe a strong
prevalence of the small values over the large ones. The
first three integers 1, 2 and 3 alone have globally a
frequency of 60\% while the other six values 4, 5, 6,
7, 8 and 9 appear only in 40\% of the cases. This
situation is actually much more general than the stock
market and it occurs in a variety of number catalogs
related to natural phenomena. The first observation of
this property traces back to S. Newcomb in 1881 but a
more precise account was given by F. Benford in 1938.
In this note we illustrate these observations with the
enlightening specific example of the stock market. We
also identify the general mechanism for the origin of
this uneven distribution in the multiplicative nature
of fluctuations in economics and in many natural
phenomena. This provides a natural explanation for the
ubiquitous presence of the Benford's law in many
different phenomena with the common element that their
fluctuations refer to a fraction of their values. This
brings us close to the problem of the spontaneous
origin of scale invariant properties in various
phenomena which is a debated question at the frontier
of different fields.",
acknowledgement = ack-nhfb,
}
@Article{Pocheau:1998:SRS,
author = "A. Pocheau",
title = "Scale ratios, statistical symmetries and
intermittency",
journal = j-EUROPHYS-LETT,
volume = "43",
number = "4",
pages = "410--415",
month = aug,
year = "1998",
CODEN = "EULEEJ",
DOI = "http://dx.doi.org/10.1209/epl/i1998-00103-6",
ISSN = "0295-5075 (print), 1286-4854 (electronic)",
ISSN-L = "0295-5075",
bibdate = "Sat Feb 16 16:02:17 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Europhysics Letters",
}
@Article{Ramsden:1998:ZLB,
author = "J. J. Ramsden and J. Vohradsk{\'y}",
title = "{Zipf}-like behavior in procaryotic protein
expression",
journal = j-PHYS-REV-E,
volume = "58",
number = "??",
pages = "7777--??",
day = "1",
month = dec,
year = "1998",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.58.7777",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.58.7777",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Schatte:1998:BLV,
author = "P. Schatte",
title = "On {Benford's law} to variable base",
journal = j-STAT-PROB-LETT,
volume = "37",
number = "4",
pages = "391--397",
day = "30",
month = mar,
year = "1998",
CODEN = "SPLTDC",
DOI = "http://dx.doi.org/10.1016/S0167-7152(97)00142-9",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "60F05 (60E15)",
MRnumber = "1624423 (99e:60072)",
MRreviewer = "Theodore P. Hill",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715297001429",
abstract = "Benford's law is studied in dependence on the base $ b
> 1 $. It can hold to large bases $b$ only
approximately. The quality of approximation is
estimated in cases of products and sums of random
variables, respectively, and in case of some
deterministic sequences. Always the approximation by
Benford's law becomes worse as $ b \to \infty $, but as
a rule also as $ b \to 1 + 0 $",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Benford's Law; Discrepancy; First-digit problem;
Mantissa distribution; Products of random variables;
Sums of random variables",
}
@Article{Slijepcevic:1998:NID,
author = "Sini{\v{s}}a Slijep{\v{c}}evi{\'c}",
title = "A Note on Initial Digits of Recurrence Sequences",
journal = j-FIB-QUART,
volume = "36",
number = "4",
pages = "305--308",
month = aug,
year = "1998",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:02:49 MDT 2011",
bibsource = "http://www.fq.math.ca/36-4.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/36-4/slijepcevic.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Troll:1998:ZLC,
author = "G. Troll and P. beim Graben",
title = "{Zipf}'s law is not a consequence of the {Central
Limit Theorem}",
journal = j-PHYS-REV-E,
volume = "57",
number = "3",
pages = "1347--1355",
day = "1",
month = feb,
year = "1998",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.57.1347",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.57.1347;
http://pre.aps.org/abstract/PRE/v57/i2/p1347_1",
abstract = "It has been observed that the rank statistics of
string frequencies of many symbolic systems (e.g., word
frequencies of natural languages) follows Zipf's law in
good approximation. We show that, contrary to claims in
the literature, Zipf's law cannot be realized by the
central limit theorem(s). The observation that a
log-normal distribution of string frequencies yields an
approximately Zipf-like rank statistics is actually
misleading. Indeed, Zipf's law for the rank statistics
is strictly equivalent to a power law distribution of
frequencies. There are two natural ways to perform the
infinite size limit for the vocabulary. The first one
is the method of choice in the literature; it makes the
upper word length bound tend to infinity and leads in
the case of a multistate Bernoulli process via a
central limit theorem to a log-normal frequency
distribution. An alternative and for text samples
actually better realizable way is to make the lower
frequency bound tend to zero. This limit procedure
leads to a power law distribution and hence to Zipf's
law --- at least for Bernoulli processes and to a very
good approximation for natural languages where it
passes the $ \chi^2 $ test. For the Bernoulli case we
will give a heuristic proof.",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Book{Wirsching:1998:DSG,
author = "G{\"u}nther J. Wirsching",
title = "The dynamical system generated by the $ 3 n + 1 $
function",
volume = "1681",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vii + 158",
year = "1998",
ISBN = "3-540-63970-5 (softcover)",
ISBN-13 = "978-3-540-63970-1 (softcover)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
LCCN = "QA3 .L28 no. 1681",
bibdate = "Mon Nov 21 08:00:54 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = ser-LNM,
URL = "http://www.loc.gov/catdir/enhancements/fy0818/97051329-d.html;
http://www.loc.gov/catdir/enhancements/fy0818/97051329-t.html",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
subject = "Sequences (Mathematics); Combinatorial probabilities;
Convergence",
}
@Article{Ausloos:1999:PMK,
author = "M. Ausloos and K. Ivanova",
title = "Precise $ (m, k) $-{Zipf} diagram analysis of
mathematical and financial time series when $ m = 6 $,
$ k = 2 $",
journal = j-PHYSICA-A,
volume = "270",
number = "3--4",
pages = "526--542",
day = "15",
month = aug,
year = "1999",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(99)00178-8",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437199001788",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Article{AyllonBurguillo:1999:PDS,
author = "Juan David {Ayll{\'o}n Burguillo} and Manuel {Perera
Dom{\'\i}nguez}",
title = "El primer d{\'\i}gito significativo. ({Spanish}) [The
first significant digit]",
journal = "{Epsilon}: Revista de la {Sociedad Andaluza de
Educaci{\'o}n Matem{\'a}tica ``Thales''}",
volume = "15",
number = "3(45)",
pages = "339--352",
month = "????",
year = "1999",
ISSN = "1131-9321",
ISSN-L = "1131-9321",
MRnumber = "K60xx",
bibdate = "Sat Feb 16 14:32:14 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "MATHEDUC.02332710",
acknowledgement = ack-nhfb,
ajournal = "{Rev. Epsil{\'o}n SAEM `Thales'}",
journal-URL = "http://thales.cica.es/epsilon/;
http://dialnet.unirioja.es/servlet/revista?codigo=504",
language = "Spanish",
remark = "Reported in \cite{Torres:2007:HDN} to contain an
extensive bibliography on Benford's Law. The publisher
does not have issues before 2003, and no electronic
copy has yet been found on the Internet. Attempts to
get this paper via Interlibrary Loan failed on the
grounds that ``We are unable to verify any owning
libraries within the United States or those that we
have ILL privileges.''",
xxauthor = "M. P. Dominguez and J. D. A. Burguillo",
xxauthor = "Manuel {Perera Dom{\'\i}nguez} and Juan David
{Ayll{\'o}n Burguillo}",
}
@Article{Barabasi:1999:ESR,
author = "Albert-L{\'a}szl{\'o} Barab{\'a}si and R{\'e}ka
Albert",
title = "Emergence of scaling in random networks",
journal = j-SCIENCE,
volume = "286",
number = "5439",
pages = "509--512",
day = "15",
month = oct,
year = "1999",
CODEN = "SCIEAS",
DOI = "http://dx.doi.org/10.1126/science.286.5439.509",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Tue Nov 15 09:57:42 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencemag.org/content/286/5439/509",
acknowledgement = ack-nhfb,
fjournal = "Science",
journal-URL = "http://www.sciencemag.org/archive/",
keywords = "power-law distribution; Zipf's Law",
}
@Article{Brakman:1999:RZT,
author = "Steven Brakman and Harry Garretsen and Charles {Van
Marrewijk} and Marianne {Van Den Berg}",
title = "The Return of {Zipf}: Towards a Further Understanding
of the Rank--Size Distribution",
journal = j-J-REG-SCI,
volume = "39",
number = "1",
pages = "183--213",
year = "1999",
DOI = "http://dx.doi.org/10.1111/1467-9787.00129",
ISSN = "0022-4146 (print), 1467-9787 (electronic)",
ISSN-L = "0022-4146",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Regional Science",
}
@Article{Coderre:1999:FDU,
author = "David Coderre",
title = "Fraud Detection Using Digital Analysis",
journal = j-EDPACS,
volume = "27",
number = "3",
pages = "1--8",
month = "????",
year = "1999",
CODEN = "EDPCDF",
DOI = "http://dx.doi.org/10.1201/1079/43249.27.3.19990901/30268.1",
ISSN = "0736-6981 (print), 1936-1009 (electronic)",
ISSN-L = "0736-6981",
bibdate = "Sat Jan 07 09:20:49 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1201/1079/43249.27.3.19990901/30268.1",
acknowledgement = ack-nhfb,
fjournal = "EDPACS",
keywords = "Benford's Law",
onlinedate = "21 Dec 2006",
}
@Article{Egghe:1999:LZM,
author = "L. Egghe",
title = "On the law of {Zipf--Mandelbrot} for multi-word
phrases",
journal = j-J-AM-SOC-INF-SCI,
volume = "50",
number = "3",
pages = "233--241",
month = "????",
year = "1999",
CODEN = "AISJB6",
DOI = "2-8;
http://dx.doi.org/10.1002/(SICI)1097-4571(1999)50:3<233::AID-ASI6>3.0.CO",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Mon Sep 10 06:09:31 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
onlinedate = "17 Feb 1999",
}
@Article{Gabaix:1999:ZLC,
author = "Xavier Gabaix",
title = "{Zipf}'s law for cities: An explanation",
journal = j-Q-J-ECON,
volume = "114",
number = "3",
pages = "739--767",
year = "1999",
CODEN = "QJECAT",
DOI = "http://dx.doi.org/10.1162/003355399556133",
ISSN = "0033-5533 (print), 1531-4650 (electronic)",
ISSN-L = "0033-5533",
bibdate = "Sat Nov 12 10:57:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0952.91059",
abstract = "Zipf's law is a very tight constraint on the class of
admissible models of local growth. It says that for
most countries the size distribution of cities
strikingly fits a power law: the number of cities with
populations greater than $S$ is proportional to $ 1 / S
$. Suppose that, at least in the upper tail, all cities
follow some proportional growth process (this appears
to be verified empirically). This automatically leads
their distribution to converge to Zipf's law.",
acknowledgement = ack-nhfb,
ajournal = "Q. J. Econ.",
classmath = "91B62 (Dynamic economic models etc.) 91B72 (Spatial
models)",
fjournal = "The Quarterly Journal of Economics",
keywords = "local growth; Zipf's law",
}
@Article{Hill:1999:DFD,
author = "Theodore P. Hill",
title = "The Difficulty of Faking Data",
journal = j-CHANCE,
volume = "12",
number = "3",
pages = "27--31",
month = "????",
year = "1999",
CODEN = "CNDCE4",
DOI = "http://dx.doi.org/10.1080/09332480.1999.10542154",
ISSN = "0933-2480 (print), 1867-2280 (electronic)",
ISSN-L = "0933-2480",
bibdate = "Tue Nov 22 18:54:44 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://amstat.tandfonline.com/doi/abs/10.1080/09332480.1999.10542154",
acknowledgement = ack-nhfb,
fjournal = "Chance: a magazine for people interested in the
analysis of data",
journal-URL = "http://chance.amstat.org/;
http://link.springer.com/journal/144;
http://www.tandfonline.com/loi/ucha20",
keywords = "Benford's Law",
xxnote = "Check: Hurlimann bibliography says v26 pp. 8--13??;
that is wrong!",
}
@Article{Hill:1999:PCS,
author = "Theodore P. Hill",
title = "Le premier chiffre significatif fait sa loi.
({French}) [{The} first significant digit makes its
law]",
journal = "La Recherche: L'actualit{\'e} des sciences",
volume = "2",
number = "316",
pages = "72--76",
month = jan,
year = "1999",
CODEN = "RCCHBV",
ISSN = "0029-5671 (print), 1625-9955 (electronic)",
ISSN-L = "0029-5671",
bibdate = "Sat Feb 16 17:51:25 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.larecherche.fr/savoirs/autre/premier-chiffre-significatif-fait-sa-loi-01-01-1999-70970",
acknowledgement = ack-nhfb,
language = "French",
xxjournal = "La Recherche Hors S{\'e}rie",
}
@Article{Huberman:1999:IGD,
author = "Bernardo A. Huberman and Lada A. Adamic",
title = "{Internet}: Growth dynamics of the {World-Wide Web}",
journal = j-NATURE,
volume = "401",
number = "6749",
pages = "131--131",
day = "9",
month = sep,
year = "1999",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/43604",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Tue Nov 15 09:52:36 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Zipf's Law",
}
@TechReport{Lowe:1999:FDL,
author = "Tomas Lowe and Sally Murphy and Justin Hayward",
title = "The First Digit Law",
type = "Report",
number = "??",
institution = "Department of Computing, Imperial College",
address = "London, UK",
month = jun,
year = "1999",
bibdate = "Wed Nov 23 16:59:50 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://users.isr.ist.utl.pt/~jmrs/research/TopicsLinks/Benford/hayward.pdf;
http://www.doc.ic.ac.uk/~jjh97/suprema/main_page.html",
acknowledgement = ack-nhfb,
lastaccess = "23 November 2011",
}
@Article{Malcai:1999:PLD,
author = "Ofer Malcai and Ofer Biham and Sorin Solomon",
title = "Power-law distributions and {L{\'e}vy}-stable
intermittent fluctuations in stochastic systems of many
autocatalytic elements",
journal = j-PHYS-REV-E,
volume = "60",
number = "2",
pages = "1299--1303",
month = aug,
year = "1999",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.60.1299",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Thu Feb 28 10:25:38 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.60.1299",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
}
@Article{Manrubia:1999:SMP,
author = "Susanna C. Manrubia and Dami{\'a}n H. Zanette",
title = "Stochastic multiplicative processes with reset
events",
journal = j-PHYS-REV-E,
volume = "59",
number = "5",
pages = "4945--4948",
month = may,
year = "1999",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.59.4945",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:25:24 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.59.4945",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
issue = "5",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's law",
}
@Article{Manrubia:1999:TDS,
author = "Susanna C. Manrubia and Dami{\'a}n H. Zanette and
Ricard V. Sol{\'e}",
title = "Transient Dynamics and Scaling Phenomena in Urban
Growth",
journal = j-FRACTALS,
volume = "7",
number = "1",
pages = "1--8",
month = mar,
year = "1999",
CODEN = "FRACEG",
DOI = "http://dx.doi.org/10.1142/S0218348X99000025",
ISSN = "0218-348X",
ISSN-L = "0218-348X",
bibdate = "Wed Feb 27 07:11:42 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.worldscientific.com/doi/abs/10.1142/S0218348X99000025",
acknowledgement = ack-nhfb,
fjournal = "Fractals",
keywords = "Zipf's Law",
}
@Article{Matthews:1999:PO,
author = "Robert Matthews",
title = "The Power of One",
journal = j-NEW-SCIENTIST,
volume = "163",
number = "2194",
pages = "27--30",
day = "10",
month = jul,
year = "1999",
CODEN = "NWSCAL",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Mon Nov 14 16:04:36 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.fortunecity.com/emachines/e11/86/one.html;
http://www.newscientist.com/article/mg16321944.600-the-power-of-one.html",
acknowledgement = ack-nhfb,
fjournal = "New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
xxISSN = "0262-4079, 0028-6664",
}
@Article{Mercik:1999:SAI,
author = "Szymon Mercik and Karina Weron and Zuzanna Siwy",
title = "Statistical analysis of ionic current fluctuations in
membrane channels",
journal = j-PHYS-REV-E,
volume = "60",
number = "6",
pages = "7343--7348",
day = "1",
month = dec,
year = "1999",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.60.7343",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.60.7343",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Nigrini:1999:AVD,
author = "Mark J. Nigrini",
title = "Adding value with digital analysis",
journal = "The Internal Auditor: Journal of the {Institute of
Internal Auditors}",
volume = "56",
number = "1",
pages = "21--23",
month = "????",
year = "1999",
CODEN = "ITAUAB",
ISSN = "0020-5745",
ISSN-L = "0020-5745",
bibdate = "Sat Feb 16 18:56:27 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Nigrini:1999:IGY,
author = "M. Nigrini",
title = "{I}'ve Got Your Number",
journal = j-J-ACCOUNTANCY,
volume = "187",
number = "??",
pages = "79--83",
month = may,
year = "1999",
CODEN = "JACYAD",
ISSN = "0021-8448 (print), 1945-0729 (electronic)",
ISSN-L = "0021-8448",
bibdate = "Mon Nov 14 16:31:40 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.aicpa.org/pubs/jofa/may1999/nigrini.htm",
acknowledgement = ack-nhfb,
fjournal = "Journal of Accountancy",
journal-URL = "http://www.journalofaccountancy.com/",
}
@Article{Nigrini:1999:PPF,
author = "Mark J. Nigrini",
title = "Peculiar patterns of first digits",
journal = j-IEEE-POT,
volume = "18",
number = "2",
pages = "24--27",
month = apr # "\slash " # may,
year = "1999",
CODEN = "IEPTDF",
DOI = "http://dx.doi.org/10.1109/45.755849",
ISSN = "0278-6648 (print), 1558-1772 (electronic)",
ISSN-L = "0278-6648",
bibdate = "Mon Nov 21 22:18:30 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Despite seeing numbers all the time only occasionally
would one say that a list of numbers seems odd. For
this to occur, the numbers are typically highly rounded
or implausible (too much of a coincidence). However
digit pattern analysis, using a computer, can produce
valuable findings not revealed at a mere glance. The
most widely cited paper on digit frequencies was
published by Frank Benford in 1938. With powerful,
low-cost personal computers, Benford's law can help us
to efficiently test the integrity of data. The first
step is to assess whether Benford's law should apply to
the data. If the data is expected to conform, then
Benford's law becomes the expected distribution.
Conformity means that the actual distribution closely
approximates the expected distribution",
acknowledgement = ack-nhfb,
fjournal = "IEEE Potentials",
}
@Article{Okuyama:1999:ZLI,
author = "K. Okuyama and M. Takayasu and H. Takayasu",
title = "{Zipf}'s law in income distribution of companies",
journal = j-PHYSICA-A,
volume = "269",
number = "1",
pages = "125--131",
day = "1",
month = jul,
year = "1999",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(99)00086-2",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437199000862",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Growth rate of assets; Income distribution; Zipf's
Law",
}
@Article{Piqueira:1999:ZLO,
author = "J. R. C. Piqueira and L. H. A. Monteiro and T. M. C.
de Magalh{\~a}es and R. T. Ramos and R. B. Sassi and E.
G. Cruz",
title = "{Zipf's Law} Organizes a Psychiatric Ward",
journal = j-J-THEOR-BIOL,
volume = "198",
number = "3",
pages = "439--443",
day = "7",
month = jun,
year = "1999",
CODEN = "JTBIAP",
DOI = "http://dx.doi.org/10.1006/jtbi.1999.0923",
ISSN = "0022-5193 (print), 1095-8541 (electronic)",
ISSN-L = "0022-5193",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022519399909232",
acknowledgement = ack-nhfb,
fjournal = "Journal of Theoretical Biology",
journal-URL = "http://www.sciencedirect.com/science/journal/00225193",
keywords = "Zipf's Law",
}
@Article{Stanley:1999:SUR,
author = "H. Eugene Stanley",
title = "Scaling, universality, and renormalization: Three
pillars of modern critical phenomena",
journal = j-REV-MOD-PHYS,
volume = "71",
number = "2",
pages = "S358--S366",
month = mar,
year = "1999",
CODEN = "RMPHAT",
DOI = "http://dx.doi.org/10.1103/RevModPhys.71.S358",
ISSN = "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
ISSN-L = "0034-6861",
bibdate = "Wed May 23 10:16:18 MDT 2012",
bibsource = "http://rmp.aps.org/toc/RMP/v71/i2;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/revmodphys1990.bib",
URL = "http://link.aps.org/doi/10.1103/RevModPhys.71.S358;
http://rmp.aps.org/abstract/RMP/v71/i2/pS358_1",
acknowledgement = ack-nhfb,
fjournal = "Reviews of Modern Physics",
journal-URL = "http://rmp.aps.org/browse",
}
@Article{Vandewalle:1999:ZAF,
author = "N. Vandewalle and M. Ausloos",
title = "The $n$-{Zipf} analysis of financial data series and
biased data series",
journal = j-PHYSICA-A,
volume = "268",
number = "1--2",
pages = "240--249",
day = "1",
month = jun,
year = "1999",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(99)00031-X",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037843719900031X",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Article{Vardi:1999:PCS,
author = "Ilan Vardi",
title = "Premiers chiffres significatifs et nombres
alg{\'e}briques. ({French}) [Significant leading digits
and algebraic numbers]",
journal = j-C-R-ACAD-SCI-I,
volume = "328",
number = "9",
pages = "749--754",
month = may,
year = "1999",
CODEN = "CASMEI",
DOI = "http://dx.doi.org/10.1016/S0764-4442(99)80265-1",
ISSN = "0764-4442 (print), 1778-3577 (electronic)",
ISSN-L = "0764-4442",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0764444299802651",
abstract = "I show that there is a meromorphic continuation of $
\sigma \log_\beta n / a < \log_\beta a n^{-s} $ to the
whole plane if and only if $ \beta $ is a Pisot number,
$ \alpha \in Q(\beta) $, and either the second largest
conjugate of $ \beta $ is real or the conjugate of $
\alpha $ corresponding to the second largest conjugate
of $ \beta $ is positive.",
acknowledgement = ack-nhfb,
fjournal = "Comptes rendus de l'Acad{\'e}mie des sciences.
S{\'e}rie I, Math{'e}matique",
keywords = "Benford's Law",
language = "French",
}
@Article{Walthoe:1999:LNO,
author = "Jon Walthoe and Robert Hunt and Mike Pearson",
title = "Looking out for number one",
journal = "Plus Magazine",
volume = "??",
number = "??",
pages = "1--9",
month = sep,
year = "1999",
DOI = "????",
bibdate = "Mon Feb 18 06:59:18 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Published by the University of Cambridge Millennium
Mathematics Project.",
URL = "http://plus.maths.org/issue9/features/benford/2pdf/index.html/op.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Blank:2000:PLC,
author = "Aharon Blank and Sorin Solomon",
title = "Power laws in cities population, financial markets and
{Internet} sites (scaling in systems with a variable
number of components)",
journal = j-PHYSICA-A,
volume = "287",
number = "1--2",
pages = "279--288",
day = "15",
month = nov,
year = "2000",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(00)00464-7",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 06:24:21 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437100004647",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Article{Drake:2000:CAA,
author = "Philip D. Drake and Mark J. Nigrini",
title = "Computer assisted analytical procedures using
{Benford's Law}",
journal = j-J-ACCOUNT-EDUC,
volume = "18",
number = "2",
pages = "127--146",
month = "Spring",
year = "2000",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/S0748-5751(00)00008-7",
ISSN = "0748-5751 (print), 1873-1996 (electronic)",
ISSN-L = "0748-5751",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0748575100000087;
http://www.sciencedirect.com/science/journal/07485751",
abstract = "This case introduces students to Benford's Law and
Digital Analysis, which can be used as an analytical
procedure and fraud detection tool. Digital Analysis
(DA) is the analysis of digit and number patterns of a
data set. Actual digit frequencies in a data set are
compared to the expected frequencies according to
Benford's Law [Benford, F. (1938). The law of the
anomalous numbers, Proceedings of the American
Philosophical Society, 78, 551 572.]. Minor differences
suggest that the data have passed a reasonableness
test, while major differences signal possible financial
statement mis-statements. After describing Benford's
Law and the basic {DA} tests, the case requires
auditing students to download {DA} software and the
actual accounts payable file of a software company from
a designated Internet site. Students then, (1) analyse
the data using three {DA} tests as an analytical
procedure in an external audit context, and (2) graph
and a report the results and audit-related conclusions.
The teaching note includes the actual findings from the
audit of that data set and guidance on using the case
in an auditing course.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Accounting Education",
keywords = "Benford's Law",
}
@Article{Lanza:2000:UDA,
author = "R. B. Lanza",
title = "Using digital analysis to detect fraud: Review of the
{DATAS\reg} statistical analysis tool",
journal = j-J-FORENSIC-ACCOUNT,
volume = "1",
number = "??",
pages = "291--296",
month = "????",
year = "2000",
CODEN = "????",
ISSN = "1524-5586",
bibdate = "Tue Nov 22 10:47:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.rtedwards.com/journals/JFA/",
acknowledgement = ack-nhfb,
fjournal = "Journal of Forensic Accounting",
}
@Article{Leemis:2000:SDS,
author = "Lawrence M. Leemis and Bruce W. Schmeiser and Diane L.
Evans",
title = "Survival Distributions Satisfying {Benford's Law}",
journal = j-AMER-STAT,
volume = "54",
number = "4",
pages = "236--241",
month = nov,
year = "2000",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRclass = "62E15 (62N05)",
MRnumber = "1803620",
bibdate = "Fri Jan 27 18:16:34 MST 2012",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326510;
http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.amstat.org/publications/tas/Leemis.htm;
http://www.jstor.org/stable/2685773",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@InProceedings{Lei:2000:EIN,
author = "Skylar Lei and Michael Smith and Giancarlo Succi",
title = "Empirical investigation of a novel approach to check
the integrity of software engineering measuring
processes",
crossref = "ACM:2000:PIC",
pages = "773--773",
year = "2000",
DOI = "http://dx.doi.org/10.1145/337180.337629",
bibdate = "Sat Feb 16 18:28:12 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@TechReport{Nigrini:2000:CA,
author = "Mark J. Nigrini",
title = "Continuous Auditing",
type = "Preprint",
institution = "Ernst \& Young Center for Auditing Research and
Advanced Technology, University of Kansas",
address = "Lawrence, KS, USA",
pages = "23",
day = "30",
month = aug,
year = "2000",
bibdate = "Sat Feb 16 18:57:40 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://aaahq.org/audit/midyear/01midyear/papers/nigrini_continuous_audit.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Book{Nigrini:2000:DAU,
author = "Mark John Nigrini",
title = "Digital analysis using {Benford}'s law: tests and
statistics for auditors",
publisher = "Global Audit Publications",
address = "Vancouver, BC, Canada",
edition = "Second",
pages = "xvii + 278",
year = "2000",
ISBN = "189449709 (??invalid ISBN??)",
ISBN-13 = "189449709 (??invalid ISBN??)",
LCCN = "????",
bibdate = "Tue Nov 22 20:48:29 MST 2011",
bibsource = "amicus.nlc-bnc.ca:210/NL;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Data processing; Auditing;
Statistical methods; Analyse num{\'e}rique;
Informatique; V{\'e}rification comptable; M{\'e}thodes
statistiques",
}
@Article{Padmanabhan:2000:CAD,
author = "Venkata N. Padmanabhan and Lili Qiu",
title = "The content and access dynamics of a busy {Web} server
(poster session)",
journal = j-SIGMETRICS,
volume = "28",
number = "1",
pages = "122--123",
month = jun,
year = "2000",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/339331.339405",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Thu Jun 26 11:31:11 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "We study the MSNBC Web site, one of the busiest in the
Internet today. We analyze the dynamics of content
creation and modification as well as client accesses.
Our key findings are (a) files tend to change little
upon modification, (b) a small set of files get
modified repeatedly, (c) file popularity follows a
Zipf-like distribution with an $ \alpha $ much larger
than reported in previous, proxy-based studies, and (d)
there is significant temporal stability in file
popularity but not much stability in the domains from
which popular content is accessed. We discuss
implications of these findings.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
journal-URL = "http://portal.acm.org/toc.cfm?id=J618",
}
@Book{Sole:2000:SLH,
author = "Ricard Vicente Sol{\'e} and Brian Goodwin",
title = "Signs of Life: How Complexity Pervades Biology",
publisher = pub-BASIC-BOOKS,
address = pub-BASIC-BOOKS:adr,
pages = "xi + 322",
year = "2000",
ISBN = "0-465-01927-7, 0-465-01928-5 (paperback)",
ISBN-13 = "978-0-465-01927-4, 978-0-465-01928-1 (paperback)",
LCCN = "QH501 .S65 2000",
bibdate = "Thu Feb 28 09:59:50 MST 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Mandelbrot; Zipf's law",
tableofcontents = "Nonlinearity, chaos, and emergence \\
Order, complexity, disorder \\
Genetic networks, cell differentiation, and development
\\
Physiology on the edge of chaos \\
Brain dynamics \\
Ants, brains, and chaos \\
The Baroque of nature \\
Life on the edge of catastrophe \\
Evolution and extinction \\
Fractal cities and market crashes",
}
@Article{Soliman:2000:BPP,
author = "Ahmed A. Soliman",
title = "{Bayes} Prediction in a {Pareto} Lifetime Model with
Random Sample Size",
journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN,
volume = "49",
number = "1",
pages = "51--62",
month = "????",
year = "2000",
CODEN = "????",
DOI = "http://dx.doi.org/10.2307/2681255",
ISSN = "0039-0526 (print), 1467-9884 (electronic)",
ISSN-L = "0039-0526",
bibdate = "Thu Jan 22 18:10:23 MST 2015",
bibsource = "http://www.jstor.org/stable/i326257;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-d-2000.bib",
URL = "http://www.jstor.org/stable/2681255",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series D
(The Statistician)",
journal-URL = "http://www.jstor.org/journals/00390526.html",
}
@Article{Stanley:2000:SIU,
author = "H. E. Stanley and L. A. N. Amaral and P. Gopikrishnan
and P. Ch. Ivanov and T. H. Keitt and V. Plerou",
title = "Scale invariance and universality: organizing
principles in complex systems",
journal = j-PHYSICA-A,
volume = "281",
number = "1--4",
pages = "60--68",
day = "15",
month = jun,
year = "2000",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(00)00195-3",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Thu Feb 28 09:52:12 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437100001953",
acknowledgement = ack-nhfb,
fjournal = "Physica A",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Tolle:2000:DDS,
author = "Charles R. Tolle and Joanne L. Budzien and Randall A.
Laviolette",
title = "Do dynamical systems follow {Benford}'s law?",
journal = j-CHAOS,
volume = "10",
number = "2",
pages = "331--336",
month = "????",
year = "2000",
CODEN = "CHAOEH",
DOI = "http://dx.doi.org/10.1063/1.166498",
ISSN = "1054-1500",
ISSN-L = "1054-1500",
bibdate = "Mon Nov 14 17:35:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2000Chaos..10..331T;
http://link.aip.org/link/chaoeh/v10/i2/p331/s1;
http://link.aip.org/link/doi/10.1063/1.166498",
abstract = "Data compiled from a variety of sources follow
Benford's law, which gives a monotonically decreasing
distribution of the first digit (1 through 9). We
examine the frequency of the first digit of the
coordinates of the trajectories generated by some
common dynamical systems. One-dimensional cellular
automata fulfill the expectation that the frequency of
the first digit is uniform. The molecular dynamics of
fluids, on the other hand, provides trajectories that
follow Benford's law. Finally, three chaotic systems
are considered: Lorenz, H{\'e}non, and R{\"o}ssler. The
Lorenz system generates trajectories that follow
Benford's law. The H{\'e}non system generates
trajectories that resemble neither the uniform
distribution nor Benford's law. Finally, the
R{\"o}ssler system generates trajectories that follow
the uniform distribution for some parameters choices,
and Benford's law for others.",
acknowledgement = ack-nhfb,
fjournal = "Chaos (Woodbury, NY)",
xxpages = "331--337",
}
@Article{Urzua:2000:SET,
author = "Carlos M. Urz{\'u}a",
title = "A simple and efficient test for {Zipf}'s law",
journal = j-ECONOM-LETT,
volume = "66",
number = "3",
pages = "257--260",
day = "1",
month = mar,
year = "2000",
CODEN = "ECLEDS",
DOI = "http://dx.doi.org/10.1016/S0165-1765(99)00215-3",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165176599002153",
ZMnumber = "0951.91059",
abstract = "This paper presents a simple and locally optimal test
for Zipf's law. Its use is illustrated in the case of
the largest US metropolitan areas. An objection to the
general relevance of that law is also presented.",
acknowledgement = ack-nhfb,
classmath = "91B82 (Statistical methods in economics) 91B74 (Models
of real-world systems)",
fjournal = "Economics Letters",
keywords = "rank-size law; Zipf's law",
}
@Article{Vogt:2000:BGS,
author = "W. Vogt",
title = "{Benford's Gesetz: Steuer- und Budgets{\"u}ndern auf
der Spur --- Zahlen l{\"u}gen nichts}. ({German})
[{Benford's Law}: tax and budget sinners lying on the
track --- Numbers do not lie]",
journal = "Schweizer Versicherung",
volume = "9",
number = "??",
pages = "27--29",
month = "????",
year = "2000",
DOI = "????",
bibdate = "Mon Feb 18 06:57:07 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "????",
acknowledgement = ack-nhfb,
journal-URL = "http://www.schweizerversicherung.ch/de/archiv_suche",
language = "German",
remark = "No ISSN assigned. Not found in journal archive on 18
February 2013.",
}
@Article{York:2000:ATB,
author = "D. York",
title = "Auditing Technique --- {Benford}'s law",
journal = j-ACCOUNTANCY,
volume = "126",
number = "1283",
pages = "126--??",
month = "????",
year = "2000",
CODEN = "ACTYAD",
ISSN = "0001-4664",
ISSN-L = "0001-4664",
bibdate = "Wed Nov 23 11:30:54 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Accountancy",
}
@Article{Axtell:2001:ZDU,
author = "R. L. Axtell",
title = "{Zipf} Distribution of {U.S.} Firm Sizes",
journal = j-SCIENCE,
volume = "293",
number = "5536",
pages = "1818--1820",
day = "7",
month = sep,
year = "2001",
CODEN = "SCIEAS",
DOI = "http://dx.doi.org/10.1126/science.1062081",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Wed Feb 27 06:38:34 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencemag.org/content/293/5536/1818",
acknowledgement = ack-nhfb,
fjournal = "Science",
journal-URL = "http://www.sciencemag.org/archive/",
keywords = "Zipf's Law",
}
@Article{Dolgikh:2001:PCS,
author = "Dmitry G. Dolgikh and Andrei M. Sukhov",
title = "Parameters of cache systems based on a {Zipf}-like
distribution",
journal = j-COMP-NET-AMSTERDAM,
volume = "37",
number = "6",
pages = "711--716",
day = "15",
month = dec,
year = "2001",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/S1389-1286(01)00243-2",
ISSN = "1389-1286 (print), 1872-7069 (electronic)",
ISSN-L = "1389-1286",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.elsevier.com/locate/issn/13891286;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.elsevier.nl/gej-ng/10/15/22/67/36/31/abstract.html;
http://www.sciencedirect.com/science/article/pii/S1389128601002432",
acknowledgement = ack-nhfb,
fjournal = "Computer Networks (Amsterdam, Netherlands: 1999)",
journal-URL = "http://www.sciencedirect.com/science/journal/13891286",
keywords = "Zipf's Law",
}
@Article{Dubinsky:2001:MFF,
author = "Bruce G. Dubinsky",
title = "Math formula fights fraud",
journal = "Legal Times of {Washington}",
volume = "XXIV",
number = "9",
pages = "??--??",
day = "26",
month = feb,
year = "2001",
ISSN = "0732-7536",
ISSN-L = "0732-7536",
bibdate = "Sat Feb 16 17:35:39 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
xxjournal = "Legal Times",
}
@Article{Gelbukh:2001:ZHL,
author = "Alexander Gelbukh and Grigori Sidorov",
title = "{Zipf} and {Heaps Laws}' Coefficients Depend on
Language",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2004",
pages = "332--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:03:22 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2004.htm;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2004/20040332.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2004/20040332.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@TechReport{Gent:2001:BL,
author = "Ian Gent and Toby Walsh",
title = "{Benford's Law}",
type = "Report",
institution = "School of Computer Science, University of St. Andrews,
and Department of Computer Science, University of
York",
address = "St. Andrews, Scotland and York, England",
pages = "7",
day = "2",
month = feb,
year = "2001",
bibdate = "Fri Nov 18 08:37:38 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.dcs.st-and.ac.uk/~apes/reports/apes-25-2001.pdf",
abstract = "Benford's Law predicts the frequency of the leading
digit in numbers met in a wide range of naturally
occurring phenomena. In data following Benford's Law,
numbers start with a small leading digit more often
those with a large leading digit. Here we demonstrate
that Benford's Law also describes a wide range of
computational phenomena. In particular, we show that a
number of different statistics associated with
computation like space and runtime often follow
Benford's Law. We also show that search cost on input
data that follows Benford's Law is often very different
to that on more uniform data. These results could be
used to improve algorithm performance (for example, for
load balancing or disk de-fragmentation), as well as to
help model algorithm performance. Benford's Law can
also be used to generate data for benchmarking
algorithms that may be more realistic than purely
random data.",
acknowledgement = ack-nhfb,
remark = "PDF file no longer at the St. Andrews URL on 18
November 2011, but recovered from
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.3357.",
}
@Article{Harremoes:2001:MEF,
author = "Peter Harremo{\"e}s and Flemming Tops{\o}e",
title = "Maximum Entropy Fundamentals",
journal = j-ENTROPY,
volume = "3",
number = "3",
pages = "191--226",
month = sep,
year = "2001",
CODEN = "ENTRFG",
DOI = "http://dx.doi.org/10.3390/e3030191",
ISSN = "1099-4300",
ISSN-L = "1099-4300",
bibdate = "Thu Feb 28 10:55:45 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.mdpi.com/1099-4300/3/3/191",
acknowledgement = ack-nhfb,
fjournal = "Entropy",
keywords = "continuity of entropy; entropy loss; exponential
family; game theoretical equilibrium; hyperbolic
distributions; information topology; maximum entropy;
minimum risk; Nash equilibrium code; partition
function; Zipf's law",
remark = "Open access journal.",
}
@Article{Hobza:2001:NBL,
author = "Tom{\'a}{\v{s}} Hobza and Igor Vajda",
title = "On the {Newcomb--Benford} law in models of statistical
data",
journal = "Revista Matem{\'a}tica Complutense",
volume = "14",
number = "2",
pages = "407--420",
year = "2001",
CODEN = "????",
ISSN = "1139-1138, 1696-8220, 1988-2807",
ISSN-L = "1139-1138",
MRclass = "62E10",
MRnumber = "1871305 (2002j:62015)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Rev. Mat. Complut.",
fjournal = "Revista Matem{\'a}tica Complutense",
}
@Article{Huang:2001:PLE,
author = "Z. F. Huang and S. Solomon",
title = "Power, {L{\'e}vy}, exponential and {Gaussian}-like
regimes in autocatalytic financial systems",
journal = j-EUR-PHYS-J-B,
volume = "20",
number = "4",
pages = "601--607",
month = apr,
year = "2001",
CODEN = "EPJBFY",
DOI = "http://dx.doi.org/10.1007/PL00011114",
ISSN = "1434-6028 (print), 1434-6036 (electronic)",
ISSN-L = "1434-6028",
bibdate = "Thu Feb 28 10:26:53 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/PL00011114",
acknowledgement = ack-nhfb,
fjournal = "European Physical Journal B: Condensed Matter and
Complex Systems",
journal-URL = "http://link.springer.com/journal/10051",
keywords = "power law; scale invariance; Zipf's law",
}
@MastersThesis{Jamain:2001:BL,
author = "Adrien Jamain",
title = "{Benford's Law}",
type = "{Master}'s thesis",
school = "Department of Mathematics, Imperial College of London
and ENSIMAG",
address = "London, UK",
pages = "????",
year = "2001",
bibdate = "Sat Feb 16 18:06:41 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Not found in Imperial College Library or COPAC
catalogs on 16 February 2013. URL link is broken too.",
URL = "http://www.math.ualberta.ca/~aberger/benford_bibliography/jamain_thesis01.pdf",
acknowledgement = ack-nhfb,
}
@Article{Jansen:2001:RNP,
author = "C. J. M. Jansen and M. M. W. Pollmann",
title = "On Round Numbers: Pragmatic Aspects of Numerical
Expressions",
journal = j-J-QUANT-LINGUISTICS,
volume = "8",
number = "3",
pages = "187--201",
month = "????",
year = "2001",
DOI = "http://dx.doi.org/10.1076/jqul.8.3.187.4095",
ISSN = "0929-6174 (print), 1744-5035 (electronic)",
ISSN-L = "0929-6174",
bibdate = "Sat Jan 07 09:51:05 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1076/jqul.8.3.187.4095",
abstract = "This paper describes and explains some regularities in
the frequency of numbers in text. An analysis of number
frequencies in text corpora in Dutch, English, German,
and French confirms the expectation that frequency is
highly dependent on two factors: magnitude and
roundness. Roundness (defined as number frequency in an
approximation context) proves to be related to three
arithmetical properties: `10-ness', `2-ness', and
`5-ness'. In predicting the frequency of numbers
irrespective of their context `$ 2 1 / 2 $-ness' should
be added to these factors, as is suggested in the work
of Sigurd (1988). The role of the four number
characteristics found in this study can be explained by
the preference of the language user for using base
numbers, and for doubling and halving quantities.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Quantitative Linguistics",
onlinedate = "09 Aug 2010",
}
@Article{Jolion:2001:IBL,
author = "Jean-Michel Jolion",
title = "Images and {Benford}'s law",
journal = j-J-MATH-IMAG-VIS,
volume = "14",
number = "1",
pages = "73--81",
year = "2001",
CODEN = "JMIVEK",
DOI = "http://dx.doi.org/10.1023/A:1008363415314",
ISSN = "0924-9907 (print), 1573-7683 (electronic)",
ISSN-L = "0924-9907",
MRclass = "94A08 (68U10)",
MRnumber = "1818436 (2001m:94007)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Imaging and Vision: JMIV",
}
@Article{Knudsen:2001:ZLC,
author = "Thorbj{\o}rn Knudsen",
title = "{Zipf}'s law for cities and beyond: the case of
{Denmark}",
journal = j-AM-J-ECON-SOCIOL,
volume = "60",
number = "1",
pages = "123--146",
month = jan,
year = "2001",
CODEN = "AJESA3",
DOI = "http://dx.doi.org/10.1111/1536-7150.00057",
ISSN = "0002-9246 (print), 1536-7150 (electronic)",
ISSN-L = "0002-9246",
bibdate = "Sat Feb 16 18:14:02 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/3487947",
acknowledgement = ack-nhfb,
fjournal = "The American Journal of Economics and Sociology",
}
@Article{Levene:2001:ZLW,
author = "Mark Levene and Jos{\'e} Borges and George Loizou",
title = "{Zipf}'s law for {Web} surfers",
journal = j-KNOWL-INFO-SYS,
volume = "3",
number = "1",
pages = "120--129",
year = "2001",
CODEN = "KISNCR",
DOI = "http://dx.doi.org/10.1007/PL00011657",
ISSN = "0219-1377",
bibdate = "Sat Nov 12 11:00:30 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0991.68622",
abstract = "One of the main activities of Web users, known as
`surfing', is to follow links. Lengthy navigation often
leads to disorientation when users lose track of the
context in which they are navigating and are unsure how
to proceed in terms of the goal of their original
query. Studying navigation patterns of Web users is
thus important, since it can lead us to a better
understanding of the problems users face when they are
surfing. We derive Zipf's rank frequency law (i.e., an
inverse power law) from an absorbing Markov chain model
of surfers' behavior assuming that less probable
navigation trails are, on average, longer than more
probable ones. In our model the probability of a trail
is interpreted as the relevance (or `value') of the
trail. We apply our model to two scenarios: in the
first the probability of a user terminating the
navigation session is independent of the number of
links he has followed so far, and in the second the
probability of a user terminating the navigation
session increases by a constant each time the user
follows a link. We analyze these scenarios using two
sets of experimental data sets showing that, although
the first scenario is only a rough approximation of
surfers' behavior, the data is consistent with the
second scenario and can thus provide an explanation of
surfers' behavior.",
acknowledgement = ack-nhfb,
classmath = "68U99 (Computing methodologies) 68P15 (Database
theory) 68P20 (Information storage and retrieval)",
fjournal = "Knowledge and Information Systems",
keywords = "Markov chain; Web navigation; Zipf's law",
}
@Article{Losee:2001:TDB,
author = "Robert M. Losee",
title = "Term dependence: a basis for {Luhn} and {Zipf}
models",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "52",
number = "12",
pages = "1019--1025",
year = "2001",
CODEN = "JASIEF",
DOI = "http://dx.doi.org/10.1002/asi.1155",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
}
@Article{Malacarne:2001:QED,
author = "L. C. Malacarne and R. S. Mendes and E. K. Lenzi",
title = "$q$-exponential distribution in urban agglomeration",
journal = j-PHYS-REV-E,
volume = "65",
number = "??",
pages = "017106",
day = "21",
month = dec,
year = "2001",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.65.017106",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.65.017106",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf--Mandelbrot law",
}
@Article{Montemurro:2001:BZM,
author = "Marcelo A. Montemurro",
title = "Beyond the {Zipf--Mandelbrot} law in quantitative
linguistics",
journal = j-PHYSICA-A,
volume = "300",
number = "3--4",
pages = "567--578",
day = "15",
month = nov,
year = "2001",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(01)00355-7",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437101003557",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@PhdThesis{Morters:2001:BGV,
author = "Peter M{\"o}rters",
title = "{Benford's Gesetz {\"u}ber die Verteilung der
Ziffern}. (German) [{Benford}'s law on the distribution
of digits]",
type = "{Habilitationsvorlesung}",
school = "????",
address = "Kaiserslauten, Germany, and Bath, UK",
pages = "4",
month = "????",
year = "2001",
bibdate = "Sat Feb 16 18:47:15 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://people.bath.ac.uk/maspm/benford.ps",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Nigrini:2001:DAU,
author = "Mark Nigrini",
title = "Digital Analysis Using {Benford's} Law: Tests and
Statistics for Auditors",
journal = j-EDPACS,
volume = "28",
number = "9",
pages = "1--2",
month = "????",
year = "2001",
CODEN = "EDPCDF",
DOI = "http://dx.doi.org/10.1201/1079/43266.28.9.20010301/30389.4",
ISSN = "0736-6981 (print), 1936-1009 (electronic)",
ISSN-L = "0736-6981",
bibdate = "Sat Jan 07 09:08:09 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1201/1079/43266.28.9.20010301/30389.4",
acknowledgement = ack-nhfb,
fjournal = "EDPACS",
onlinedate = "21 Dec 2006",
}
@Article{Pietronero:2001:EUD,
author = "L. Pietronero and E. Tosatti and V. Tosatti and A.
Vespignani",
title = "Explaining the uneven distribution of numbers in
nature: the laws of {Benford} and {Zipf}",
journal = j-PHYSICA-A,
volume = "293",
number = "1--2",
pages = "297--304",
day = "1",
month = apr,
year = "2001",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(00)00633-6",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2001PhyA..293..297P;
http://www.sciencedirect.com/science/article/pii/S0378437100006336",
abstract = "The distribution of first digits in numbers series
obtained from very different origins shows a marked
asymmetry in favor of small digits that goes under the
name of Benford's law. We analyze in detail this
property for different data sets and give a general
explanation for the origin of the Benford's law in
terms of multiplicative processes. We show that this
law can be also generalized to series of numbers
generated from more complex systems like the catalogs
of seismic activity. Finally, we derive a relation
between the generalized Benford's law and the popular
Zipf's law which characterize the rank order statistics
and has been extensively applied to many problems
ranging from city population to linguistics.",
acknowledgement = ack-nhfb,
fjournal = "Physica A: Statistical Mechanics and its
Applications",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Reed:2001:PZO,
author = "William J. Reed",
title = "The {Pareto}, {Zipf} and other power laws",
journal = j-ECONOM-LETT,
volume = "74",
number = "1",
pages = "15--19",
day = "20",
month = dec,
year = "2001",
CODEN = "ECLEDS",
DOI = "http://dx.doi.org/10.1016/S0165-1765(01)00524-9",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165176501005249",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
keywords = "Zipf's Law",
}
@TechReport{Scott:2001:BLE,
author = "P. D. Scott and M. Fasli",
title = "{Benford's Law}: An Empirical Investigation and a
Novel Explanation",
type = "CSM Technical Report",
number = "349",
institution = "Department of Computer Science, University Essex",
address = "Colchester, UK",
day = "26",
month = oct,
year = "2001",
bibdate = "Tue Nov 22 21:05:22 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.essex.ac.uk/csee/research/publications/technicalreports/2001/CSM-349.pdf",
acknowledgement = ack-nhfb,
}
@Article{Sellke:2001:CVT,
author = "Thomas Sellke and M. J. Bayarri and James O. Berger",
title = "Calibration of $p$ Values for Testing Precise Null
Hypotheses",
journal = j-AMER-STAT,
volume = "55",
number = "1",
pages = "62--71",
month = feb,
year = "2001",
CODEN = "ASTAAJ",
DOI = "http://dx.doi.org/10.1198/000313001300339950",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Jan 27 18:16:34 MST 2012",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326511;
http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.amstat.org/publications/tas/Sellke.htm;
http://www.jstor.org/stable/2685531;
http://www.tandfonline.com/doi/abs/10.1198/000313001300339950",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Snyder:2001:SAO,
author = "Mark A. Snyder and James H. Curry and Anne M.
Dougherty",
title = "Stochastic aspects of one-dimensional discrete
dynamical systems: {Benford}'s law",
journal = j-PHYS-REV-E,
volume = "64",
number = "2",
pages = "026222",
month = aug,
year = "2001",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.64.026222",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Mon Nov 14 17:44:15 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2001PhRvE..64b6222S;
http://pre.aps.org/abstract/PRE/v64/i2/e026222",
abstract = "Benford's law owes its discovery to the ``Grubby Pages
Hypothesis,'' a 19th century observation made by Simon
Newcomb that the beginning pages of logarithm books
were grubbier than the last few pages, implying that
scientists referenced the values toward the front of
the books more frequently. If a data set satisfies
Benford's law, then its significant digits will have a
logarithmic distribution, which favors smaller
significant digits. In this article we demonstrate two
ways of creating discrete one-dimensional dynamical
systems that satisfy Benford's law. We also develop a
numerical simulation methodology that we use to study
dynamical systems when analytical results are not
readily available.",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
pagecount = "5",
}
@InCollection{Solomon:2001:SPZ,
author = "Sorin Solomon and Peter Richmond",
booktitle = "Economics with heterogeneous interacting agents
({Marseille}, 2000)",
title = "Stability of {Pareto--Zipf} law in non-stationary
economies",
volume = "503",
publisher = pub-SV,
address = pub-SV:adr,
pages = "141--159",
year = "2001",
MRclass = "91B28 (91B62)",
MRnumber = "1838925",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Lecture Notes in Econom. and Math. Systems",
acknowledgement = ack-nhfb,
}
@Article{Zanette:2001:VTC,
author = "Dami{\'a}n H. Zanette and Susanna C. Manrubia",
title = "Vertical transmission of culture and the distribution
of family names",
journal = j-PHYSICA-A,
volume = "295",
number = "1--2",
pages = "1--8",
day = "1",
month = jun,
year = "2001",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(01)00046-2",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:03:20 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437101000462",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Article{Abe:2002:STE,
author = "Sumiyoshi Abe",
title = "Stability of {Tsallis} entropy and instabilities of
{R{\'e}nyi} and normalized {Tsallis} entropies: a basis
for $q$-exponential distributions",
journal = j-PHYS-REV-E,
volume = "66",
number = "??",
pages = "046134",
day = "24",
month = oct,
year = "2002",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.66.046134",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.66.046134",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Anonymous:2002:ZLM,
author = "Anonymous",
title = "{Zipf}'s law and maximum sustainable growth",
journal = j-STAT-PROB-LETT,
volume = "56",
number = "2",
pages = "??--??",
day = "15",
month = jan,
year = "2002",
CODEN = "SPLTDC",
DOI = "http://dx.doi.org/10.1016/j.jedc.2013.02.004",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165188913000341",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Zipf's Law",
onlinedate = "19 February 2013",
}
@InProceedings{Bhattacharya:2002:KBT,
author = "S. Bhattacharya",
editor = "????",
booktitle = "9th World Congress of Accounting Historians, Deakin
University, Melbourne, Australia July 30--August 3,
2002",
title = "From {Kautilya} to {Benford} --- Trends in Forensic
and Investigative Accounting",
publisher = "Accounting Association of Australia and New Zealand",
address = "????",
pages = "??--??",
year = "2002",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 17:22:29 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
journal-URL = "http://ach.sagepub.com/",
remark = "I cannot find the published proceedings in online
catalogs or bookstores, or in the Deakin University
library catalogs. Where only selected papers published
from the conference in the journal Accounting
History??",
review-doi = "http://dx.doi.org/10.1177/103237320200700207",
review-url = "http://dro.deakin.edu.au/view/DU:30012663;
http://www.highbeam.com/doc/1G1-97484707.html",
}
@Article{Bolton:2002:SFD,
author = "Richard J. Bolton and David J. Hand",
title = "Statistical Fraud Detection: A Review",
journal = j-STAT-SCI,
volume = "17",
number = "3",
pages = "235--255",
month = aug,
year = "2002",
CODEN = "STSCEP",
ISSN = "0883-4237",
ISSN-L = "0883-4237",
bibdate = "Fri May 30 12:48:50 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/statsci.bib",
URL = "http://projecteuclid.org/euclid.ss/1042727940",
acknowledgement = ack-nhfb,
fjournal = "Statistical Science",
journal-URL = "http://projecteuclid.org/all/euclid.ss",
}
@Article{Brown:2002:ICF,
author = "Philip Brown and Angeline Chua and Jason Mitchell",
title = "The influence of cultural factors on price clustering:
Evidence from {Asia Pacific} stock markets",
journal = "Pacific-Basin Finance Journal",
volume = "10",
number = "3",
pages = "307--332",
year = "2002",
DOI = "http://dx.doi.org/10.1016/S0927-538X(02)00049-5",
ISSN = "0927-538X",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "13th Annual PACAP/FMA Finance Conference",
URL = "http://www.sciencedirect.com/science/article/pii/S0927538X02000495",
abstract = "Price clustering is the tendency of prices to be
observed more frequently at some numbers than others.
It increases with haziness, or imprecision, about
underlying value. Most research on price clustering has
been conducted in Western financial markets, where
there is manifest preference for trading at round
numbers. We focus on number preferences under Chinese
culture. Many Chinese believe some numbers are unlucky
and to be avoided. For instance, the number 4 is
inauspicious because the Cantonese pronunciation of 4
is similar to the phrase to die . We first document
clustering of daily closing prices on six Asia Pacific
stock markets, three with predominantly Chinese
populations. Next, we fit binomial logit models within
these markets to estimate the association between
structural and economic factors, and culture, on price
clustering. We find some support for the influence of
Chinese culture and superstition on year-round number
preferences of traders, but it is located solely in the
Hong Kong market. Furthermore, in the Hong Kong market
Chinese culture and superstition help explain the
increased avoidance of the number 4 during the
auspicious Chinese New Year, Dragon Boat and Mid-Autumn
festivals.",
acknowledgement = ack-nhfb,
keywords = "Attraction; Benford's Law; Haziness; Negotiation;
Price clustering",
}
@TechReport{Diekmann:2002:DFM,
author = "Andreas Diekmann",
title = "{Diagnose von Fehlerquellen und methodische
Qualit{\"a}t in der sozialwissenschaftlichen
Forschung}. ({German}) [{Diagnosis} of errors and
methodological quality in social science research]",
type = "Report",
number = "ITA-02-04",
institution = "Institut f{\"u}r Technikfolgen-Absch{\"a}tzung",
address = "Vienna, Austria",
pages = "????",
year = "2002",
bibdate = "Thu Nov 17 19:11:00 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{FerreriCancho:2002:ZLR,
author = "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}",
title = "{Zipf}'s law and random texts",
journal = j-ADV-COMPLEX-SYST,
volume = "5",
number = "1",
pages = "1--6",
year = "2002",
CODEN = "????",
DOI = "http://dx.doi.org/10.1142/S0219525902000468",
ISSN = "0219-5259",
bibdate = "Sat Nov 12 11:00:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "1090.91595",
abstract = "Random-text models have been proposed as an
explanation for the power law relationship between word
frequency and rank, the so-called Zipf's law. They are
generally regarded as null hypotheses rather than
models in the strict sense. In this context, recent
theories of language emergence and evolution assume
this law as a priori information with no need of
explanation. Here, random texts and real texts are
compared through (a) the so-called lexical spectrum and
(b) the distribution of words having the same length.
It is shown that real texts fill the lexical spectrum
much more efficiently and regardless of the word
length, suggesting that the meaningfulness of Zipf's
law is high.",
acknowledgement = ack-nhfb,
classmath = "91F20 (Linguistics)",
fjournal = "Advances in Complex Systems",
journal-URL = "http://www.worldscinet.com/acs/acs.shtml",
keywords = "Human language; monkey languages; random texts;
scaling; Zipf's law",
}
@Article{Gottwald:2002:NBL,
author = "Georg A. Gottwald and Matthew Nicol",
title = "On the nature of {Benford's Law}",
journal = j-PHYSICA-A,
volume = "303",
number = "3--4",
pages = "387--396",
day = "15",
month = jan,
year = "2002",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(01)00497-6",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "60C05 (28D05 60E05 82B05)",
MRnumber = "1917635 (2003d:60015)",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://adsabs.harvard.edu/abs/2002PhyA..303..387G;
http://www.sciencedirect.com/science/article/pii/S0378437101004976",
abstract = "We study multiplicative and affine sequences of real
numbers defined by $ N(j + 1) = \zeta (j) N(j) + \eta
(j) $, where \{\zeta(j)\} and \{\eta(j)\} are sequences
of positive real numbers (in the multiplicative case $
\eta (j) = 0 $ for all $j$). We investigate the
conditions under which the leading digits $k$ of
\{N(j)\} have the following probability distribution,
known as Benford's Law, $ P(k) = \log_{10}((k + 1) /
k)$. We present two main results. First, we show that
contrary to the usual assumption in the literature,
\{\zeta(j)\} does not necessarily need to come from a
chaotic or independent random process for Benford's Law
to hold. The multiplicative driving force may be a
deterministic quasiperiodic or even periodic forcing.
Second, we give conditions under which the distribution
of the first digits of an affine process displays
Benford's Law. Our proofs use techniques from ergodic
theory.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Benford's Law; Law of Anomalous Numbers;
Multiplicative process; Scaling laws; Zipf's Law",
}
@Article{Hasan:2002:ADA,
author = "Bassam Hasan",
title = "Assessing data authenticity with {Benford}'s law",
journal = "Information Systems Control Journal",
volume = "6",
pages = "??--??",
year = "2002",
CODEN = "ISYJFS",
ISSN = "1526-7407",
bibdate = "Sat Feb 16 17:45:21 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.isaca.org/Journal/Past-Issues/2002/Volume-6/Pages/Assessing-Data-Authenticity-With-Benfords-Law.aspx",
acknowledgement = ack-nhfb,
journal-URL = "http://www.isaca.org/",
remark = "Journal publication ceased at volume 6 in 2008,
according to one library catalog, but volumes up to
2013 are available at journal Web site.",
}
@InProceedings{Hill:2002:RAB,
author = "T. P. Hill",
editor = "????",
booktitle = "Conference, Leiden University",
title = "Recent applications of {Benford}'s law",
publisher = "????",
address = "????",
pages = "??--??",
year = "2002",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 17:55:46 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Hoyle:2002:MSM,
author = "David C. Hoyle and Magnus Rattray and Ray Jupp and
Andrew Brass",
title = "Making sense of microarray data distributions",
journal = j-BIOINFORMATICS,
volume = "18",
number = "4",
pages = "576--584",
month = apr,
year = "2002",
ISSN = "1367-4803 (print), 1367-4811 (electronic)",
ISSN-L = "1367-4803",
bibdate = "Fri Nov 25 11:16:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Bioinformatics",
keywords = "Benford's Law; mRNA transcription data",
}
@Article{Jones:2002:LDR,
author = "B. K. Jones",
title = "Logarithmic distributions in reliability analysis",
journal = j-MICROELECT-RELIABILITY,
volume = "42",
number = "4--5",
pages = "779--786",
month = apr # "\slash " # may,
year = "2002",
CODEN = "MCRLAS",
DOI = "http://dx.doi.org/10.1016/S0026-2714(02)00031-8",
ISSN = "0026-2714 (print), 1872-941X (electronic)",
ISSN-L = "0026-2714",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0026271402000318",
abstract = "Real-life systems are complex, with many independent
parameters which can affect the system. Their behaviour
can therefore be very variable. This is especially true
of the more involved processes which occur in
reliability and degradation processes. However, there
are some characteristics which are observed which can
be understood simply because they are characteristic of
complex systems. These include distributions that are
very often logarithmic rather than uniform, log normal
failure distributions and $ 1 g / f $ noise. A wide
variety of diverse examples is given to illustrate the
common occurrence of such observations together with
the underlying unifying themes. There are several basic
reasons for the origin of logarithmic distributions.
One is that they arise from multiplicative processes.
Another is that although basic science is often
introduced as linear, with non-linear effects added as
a correction, complex systems are often inherently
non-linear. This produces multiplicative effects, such
as harmonic generation and fractal behaviour.",
acknowledgement = ack-nhfb,
fjournal = "Microelectronics and Reliability",
keywords = "Benford's Law; Pareto distribution; Zipf's Law",
}
@Article{Kawamura:2002:UZL,
author = "Kenji Kawamura and Naomichi Hatano",
title = "Universality of {Zipf}'s law",
journal = j-J-PHYS-SOC-JAP,
volume = "71",
number = "5",
pages = "1211--1213",
year = "2002",
CODEN = "JUPSAU",
DOI = "http://dx.doi.org/10.1143/JPSJ.71.1211",
ISSN = "0031-9015 (print), 1347-4073 (electronic)",
ISSN-L = "0031-9015",
bibdate = "Sat Nov 12 11:00:54 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jpsj.ipap.jp/",
ZMnumber = "1063.60114",
abstract = "The aim of the present paper is to propose and
simulate a simple and generic model that reproduces
Zipf's law. In the proposed model, the time evolution
is considered to be a random walk in the logarithmic
scale reflecting the company asset distribution and/or
the evolution of city populations (e.g. Zipf's law for
income distribution asserts that the size and number of
companies are in inverse proportional relationship).
The paper explains theoretically and shows by numerical
simulation that the introduced model of Zipf's law has
a very robust behaviour when applied to various natural
and social phenomena. The authors do not investigate
the famous case of Zipf's law application to the
frequency of English words, but they speculate that
this case might be also explained within the same time
development of the proposed model.",
acknowledgement = ack-nhfb,
classmath = "60J60 (Diffusion processes) 60J70 (Appl. of diffusion
theory) 76R50 (Diffusion) 82C24 (Interface problems
(dynamic and non-equilibrium))",
fjournal = "Journal of the Physical Society of Japan",
keywords = "city population evolution; company asset distribution;
diffusion; generic model of Zipf's law; natural and
social phenomena; random walk in logarithmic scale",
ZMreviewer = "Neculai Curteanu (Ia\c si)",
}
@TechReport{Kreiner:2002:FDL,
author = "W. A. Kreiner",
title = "First digit law",
type = "Preprint",
institution = "Abteilung Chemische Physik, Arbeitsgruppe
Laseranwendungen, Universit{\"a}t Ulm",
address = "Ulm, Germany",
pages = "7",
day = "3",
month = may,
year = "2002",
bibdate = "Sat Feb 16 18:18:49 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://vts.uni-ulm.de/docs/2002/1441/vts_1441.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; First Digit Law; Newcomb; Statistisches
Fraktal",
language = "German",
}
@Article{Li:2002:ZLI,
author = "Wentian Li and Yaning Yang",
title = "{Zipf's Law} in Importance of Genes for Cancer
Classification Using Microarray Data",
journal = j-J-THEOR-BIOL,
volume = "219",
number = "4",
pages = "539--551",
day = "21",
month = dec,
year = "2002",
CODEN = "JTBIAP",
DOI = "http://dx.doi.org/10.1006/jtbi.2002.3145",
ISSN = "0022-5193 (print), 1095-8541 (electronic)",
ISSN-L = "0022-5193",
MRclass = "92C40 (92D10)",
MRnumber = "2044066",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022519302931450",
acknowledgement = ack-nhfb,
fjournal = "Journal of Theoretical Biology",
journal-URL = "http://www.sciencedirect.com/science/journal/00225193",
keywords = "Zipf's Law",
}
@Book{Livio:2002:GRS,
author = "Mario Livio",
title = "The golden ratio: the story of phi, the world's most
astonishing number",
publisher = "Broadway Books",
address = "New York, NY, USA",
pages = "viii + 294",
year = "2002",
ISBN = "0-7679-0815-5",
ISBN-13 = "978-0-7679-0815-3",
LCCN = "QA466 .L58 2002",
bibdate = "Tue Jul 08 12:29:44 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Benford's Law is treated on pages 231--237.",
price = "US\$24.95, CAN\$37.95",
acknowledgement = ack-nhfb,
}
@InProceedings{Manaris:2002:PTR,
author = "B. Manaris and T. Purewal and C. McCormick",
editor = "{IEEE}",
booktitle = "Proceedings: IEEE SoutheastCon 2002: April 5--7, 2002,
Embassy Suites Hotel, Columbia, South Carolina, USA",
title = "Progress Towards Recognizing and Classifying Beautiful
Music with Computers: {MIDI}-Encoded Music and the
{Zipf-Mandelbrot Law}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "52--57",
year = "2002",
DOI = "http://dx.doi.org/10.1109/.2002.995557",
ISBN = "0-7803-7252-2",
ISBN-13 = "978-0-7803-7252-8",
LCCN = "TK7801 .I56 2002",
bibdate = "Mon Feb 18 10:40:27 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=7814",
acknowledgement = ack-nhfb,
bookpages = "xviii + 482",
}
@Article{Mochty:2002:AMI,
author = "L. Mochty",
title = "{Die Aufdeckung von Manipulationen im Rechnungswesen
--- Was leistet das Benford's Law?}. ({German}) [{The}
disclosure of accounting manipulations --- what does
{Benford's Law} mean?]",
journal = "Die Wirtschaftspr{\"u}fung",
volume = "14",
number = "??",
pages = "725--736",
month = "????",
year = "2002",
CODEN = "????",
ISSN = "0043-6313",
ISSN-L = "0043-6313",
bibdate = "Thu Nov 17 19:20:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Book{Newman:2002:ME,
author = "M. E. J. (Mark E. J.) Newman and Richard G. Palmer",
title = "Modeling extinction",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xii + 102",
year = "2002",
ISBN = "0-19-515946-2 (paperback), 0-19-515945-4 (hardcover)",
ISBN-13 = "978-0-19-515946-2 (paperback), 978-0-19-515945-5
(hardcover)",
LCCN = "QH78 .N48 2002",
bibdate = "Thu Feb 28 10:36:25 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
library.ox.ac.uk:210/ADVANCE",
series = "Santa Fe Institute studies in the sciences of
complexity",
acknowledgement = ack-nhfb,
keywords = "power law; Zipf's law",
subject = "Extinction (Biology); Statistical methods;
Mathematical models",
}
@Misc{Popescu:2002:LNZ,
author = "Ioan-Iovitz Popescu",
title = "On the {Lavelette}'s nonlinear {Zipf}'s law",
howpublished = "Web preprint.",
month = feb,
year = "2002",
bibdate = "Sat Feb 16 19:02:15 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://alpha2.infim.ro/~ltpd/Zipf's_Law.html",
acknowledgement = ack-nhfb,
}
@Article{Reed:2002:GFG,
author = "William J. Reed and Barry D. Hughes",
title = "From gene families and genera to incomes and
{Internet} file sizes: Why power laws are so common in
nature",
journal = j-PHYS-REV-E,
volume = "66",
number = "6",
pages = "067103",
month = dec,
year = "2002",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.66.067103",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Wed Feb 27 06:58:05 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.66.067103",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Pareto's Law; rank-size property; Zipf's Law",
pagecount = "4",
}
@Article{Sandron:2002:DPC,
author = "Fr{\'e}d{\'e}ric Sandron",
title = "Do populations conform to the {Law of Anomalous
Numbers}?",
journal = "Population",
volume = "57",
number = "4--5",
pages = "755--761",
month = "????",
year = "2002",
CODEN = "????",
DOI = "????",
ISSN = "1169-1018",
ISSN-L = "1169-1018",
bibdate = "Sat Feb 16 19:08:50 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Translation from French by S. R. Hayford.",
URL = "http://www.cairn.info/article_p.php?ID_ARTICLE=POPE_204_0753",
acknowledgement = ack-nhfb,
journal-URL = "http://www.jstor.org/journals/11691018.html",
}
@Article{Sandron:2002:PSE,
author = "Fr{\'e}d{\'e}ric Sandron",
title = "Les populations suivent-elles la loi des nombres
anomaux? ({French}). [{Do} populations conform to the
{Law of Anomalous Numbers}?]",
journal = "Population ({French} edition)",
volume = "57",
number = "4--5",
pages = "761--768",
month = "????",
year = "2002",
CODEN = "POPUAQ",
DOI = "????",
ISSN = "0032-4663 (print), 1957-7966 (electronic)",
ISSN-L = "0032-4663",
bibdate = "Sat Feb 16 19:08:50 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.persee.fr/web/revues/home/prescript/article/pop_0032-4663_2002_num_57_4_16873",
acknowledgement = ack-nhfb,
language = "French",
}
@TechReport{Seaman:2002:BLB,
author = "R. S. Seaman",
title = "{Benford}'s law and and background field errors in
data assimilation",
type = "Preprint",
institution = "Bureau of Meteorology Research Centre",
address = "Melbourne, Australia",
month = "????",
year = "2002",
bibdate = "Sun Feb 17 14:01:22 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://amm.bom.gov.au/amoj/docs/2002/seaman.pdf",
acknowledgement = ack-nhfb,
}
@Article{Seaman:2002:RBL,
author = "R. S. Seaman",
title = "The relevance of {Benford's Law} to background field
errors in data assimilation",
journal = "Australian Meteorological Magazine",
volume = "51",
number = "1",
pages = "25--33",
month = "????",
year = "2002",
CODEN = "AMMGAS",
ISSN = "0004-9743",
ISSN-L = "0004-9743",
bibdate = "Mon Nov 14 16:08:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.bom.gov.au/amm/docs/2002/seaman.pdf;
http://www.bom.gov.au/amm/docs/2002/seaman_hres.pdf",
acknowledgement = ack-nhfb,
ajournal = "Aust. Met. Mag.",
ajournal-2 = "Aust. Meteorol. Mag.",
fjournal = "Australian Meteorological Magazine",
journal-URL = "http://www.bom.gov.au/amm/",
}
@Article{Taylor:2002:STD,
author = "Rosemary N. Taylor and Damian J. McEntegart and
Eleanor C. Stillman",
title = "Statistical techniques to detect fraud and other data
irregularities in clinical questionnaire data",
journal = "Drug Information Journal",
volume = "36",
number = "1",
pages = "115--125",
month = jan,
year = "2002",
DOI = "http://dx.doi.org/10.1177/009286150203600115",
ISSN = "0092-8615",
ISSN-L = "0092-8615",
bibdate = "Mon Feb 18 06:42:24 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.diahome.org/DIAHome/resources/content.aspx?type=eopdf&file=%2Fproductfiles%2F8357%2Fdiaj_11524.pdf????",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{VanCaneghem:2002:EMI,
author = "T. {Van Caneghem}",
title = "Earnings Management Induced by Cognitive Reference
Points",
journal = "The British Accounting Review",
volume = "34",
number = "2",
pages = "167--178",
year = "2002",
DOI = "http://dx.doi.org/10.1006/bare.2002.0190",
ISSN = "0890-8389 (print), 1095-8347 (electronic)",
ISSN-L = "0890-8389",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0890838902901903",
abstract = "Previous studies (Carslaw, 1988; Thomas, 1989;
Niskanen \& Keloharju, 2000) have shown that companies'
managers tend to round-up the first digits of reported
earnings (i.e. for companies reporting profits).
According to Carslaw (1988), this type of behaviour is
inspired by the existence of the so-called `\$1.99'
phenomenon where a price of \$1.99 is perceived as
being abnormally lower than one of \$2.00. In the
current study, we try to determine whether managers of
UK-listed companies also engage in this type of
`earnings rounding-up behaviour'. Analogous to the
earlier studies, our study compares observed and
expected frequencies for the second-from-the-left digit
in reported earnings. Our results suggest that managers
of UK-listed companies tend to round-up reported
pre-tax income, in a way that increases the first digit
by one, when they are faced with a nine in the
second-from-the-left position for this particular
earnings measure. The major contribution of the current
study is that it introduces discretionary accruals in
this line of research. Discretionary accruals were
estimated using both the Jones model (1991) and the
modified Jones model as proposed by Dechow et al.
(1995). Our results clearly suggest that discretionary
accruals are used in order to round-up reported
earnings figures. Moreover, discretionary accruals
enabled us to increase the power of the tests used in
previous studies.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Yeh:2002:SMZ,
author = "Hsiaw-Chan Yeh",
title = "Six multivariate {Zipf} distributions and their
related properties",
journal = j-STAT-PROB-LETT,
volume = "56",
number = "2",
pages = "131--141",
day = "15",
month = jan,
year = "2002",
CODEN = "SPLTDC",
DOI = "http://dx.doi.org/10.1016/S0167-7152(01)00149-3",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "62H10",
MRnumber = "1881166 (2002m:62084)",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715201001493",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Zipf's Law",
}
@Article{Abdel-All:2003:GPP,
author = "N. H. Abdel-All and M. A. W. Mahmoud and H. N.
Abd-Ellah",
title = "Geometrical properties of {Pareto} distribution",
journal = j-APPL-MATH-COMP,
volume = "145",
number = "2--3",
pages = "321--339",
day = "25",
month = dec,
year = "2003",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Jan 9 08:41:12 MST 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Alvarez-Ramirez:2003:ZMS,
author = "Jose Alvarez-Ramirez and Monica Meraz and Gustavo
Gallegos",
title = "{Zipf--Mandelbrot} scaling law for world track
records",
journal = j-PHYSICA-A,
volume = "328",
number = "3--4",
pages = "545--560",
day = "15",
month = oct,
year = "2003",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(03)00579-X",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037843710300579X",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Book{Anastasi:2003:NFI,
author = "Joe Anastasi",
title = "The new forensics: investigating corporate fraud and
the theft of intellectual property",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiv + 270",
year = "2003",
ISBN = "0-471-26994-8 (hardcover)",
ISBN-13 = "978-0-471-26994-6 (hardcover)",
LCCN = "HV8079.W47 A5 2003",
bibdate = "Tue Nov 22 11:42:36 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/bios/wiley044/2003001697.html;
http://www.loc.gov/catdir/description/wiley037/2003001697.html;
http://www.loc.gov/catdir/toc/wiley031/2003001697.html",
acknowledgement = ack-nhfb,
remark = "Brief mention of Benford's Law on pp. 184--185.",
subject = "white collar crime investigation; data processing;
case studies; fraud investigation; forensic accounting;
computer security",
}
@Article{Ausloos:2003:SIZ,
author = "M. Ausloos and Ph. Bronlet",
title = "Strategy for investments from {Zipf} law(s)",
journal = j-PHYSICA-A,
volume = "324",
number = "1--2",
pages = "30--37",
day = "1",
month = jun,
year = "2003",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(02)01845-9",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "91B82",
MRnumber = "2030919",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "International Econophysics Conference IEC2002 (Bali)",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437102018459",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Book{Baldi:2003:MIW,
author = "Pierre Baldi and Paolo Frasconi and Padhraic Smyth",
title = "Modeling the {Internet} and the {Web}: probabilistic
methods and algorithms",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xix + 285",
year = "2003",
ISBN = "0-470-86492-3 (e-book), 0-470-84906-1",
ISBN-13 = "978-0-470-86492-0 (e-book), 978-0-470-84906-4",
LCCN = "TK5105.875.I57 B35 2003eb",
bibdate = "Fri Jun 3 10:03:23 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/pagerank.bib",
acknowledgement = ack-nhfb,
subject = "Internet; Mathematical models; Telecommunication;
Traffic; World Wide Web; Cyberspace; Probabilities;
Computers; Web; General; Networking; Intranets and
Extranets",
tableofcontents = "Mathematical Background \\
Probability and Learning from a Bayesian Perspective
\\
Parameter Estimation from Data \\
Basic principles \\
A simple die example \\
Mixture Models and the Expectation Maximization
Algorithm \\
Graphical Models \\
Bayesian networks \\
Belief propagation \\
Learning directed graphical models from data \\
Classification \\
Clustering \\
Power-Law Distributions \\
Scale-free properties (80/20 rule) \\
Applications to Languages: Zipf's and Heaps' Laws \\
Origin of power-law distributions and Fermi's model \\
Basic WWW Technologies \\
Web Documents \\
SGML and HTML \\
General structure of an HTML document \\
Links \\
Resource Identifiers: URI, URL, and URN \\
Protocols \\
Reference models and TCP/IP \\
The domain name system \\
The Hypertext Transfer Protocol \\
Programming examples \\
Log Files \\
Search Engines \\
Coverage \\
Basic crawling \\
Web Graphs \\
Internet and Web Graphs \\
Power-law size \\
Power-law connectivity \\
Small-world networks \\
Power law of PageRank \\
The bow-tie structure \\
Generative Models for the Web Graph and Other Networks
\\
Web page growth \\
Lattice perturbation models: between order and disorder
\\
Preferential attachment models, or the rich get richer
\\
Copy models \\
PageRank models \\
Applications \\
Distributed search algorithms \\
Subgraph patterns and communities \\
Robustness and vulnerability \\
Notes and Additional Technical References \\
Text Analysis \\
Indexing \\
Compression techniques \\
Lexical Processing \\
Tokenization",
}
@TechReport{Berger:2003:BLP,
author = "Arno Berger",
title = "{Benford}'s law in power-like nonautonomous dynamical
systems",
type = "Preprint",
institution = "Vienna University of Technology",
address = "Vienna, Austria",
year = "2003",
bibdate = "Sat Feb 16 17:18:18 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Canessa:2003:TAFa,
author = "Enrique Canessa",
title = "Theory of Analogous Force on Number Sets",
journal = "ArXiv e-prints",
year = "2003",
bibdate = "Mon Nov 21 06:56:01 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/cond-mat/0307703",
abstract = "A general statistical thermodynamic theory that
considers given sequences of $x$-integers to play the
role of particles of known type in an isolated elastic
system is proposed. By also considering some explicit
discrete probability distributions $ p_x $ for natural
numbers, we claim that they lead to a better
understanding of probabilistic laws associated with
number theory. Sequences of numbers are treated as the
size measure of finite sets. By considering $ p_x $ to
describe complex phenomena, the theory leads to derive
a distinct analogous force $ f_x $ on number sets
proportional to $ (\frac {\partial p_x}{\partial x})_T
$ at an analogous system temperature $T$. In
particular, this yields to an understanding of the
uneven distribution of integers of random sets in terms
of analogous scale invariance and a screened inverse
square force acting on the significant digits. The
theory also allows to establish recursion relations to
predict sequences of Fibonacci numbers and to give an
answer to the interesting theoretical question of the
appearance of the Benford's law in Fibonacci numbers. A
possible relevance to prime numbers is also analyzed.",
acknowledgement = ack-nhfb,
remark = "To appear in Phys. A.",
}
@Article{Canessa:2003:TAFb,
author = "Enrique Canessa",
title = "Theory of analogous force on number sets",
journal = j-PHYSICA-A,
volume = "328",
number = "1--2",
pages = "44--52",
month = oct,
year = "2003",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(03)00526-0",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437103005260",
abstract = "A general statistical thermodynamic theory that
considers given sequences of $x$-integers to play the
role of particles of known type in an isolated elastic
system is proposed. By also considering some explicit
discrete probability distributions $ p_x $ for natural
numbers, we claim that they lead to a better
understanding of probabilistic laws associated with
number theory. Sequences of numbers are treated as the
size measure of finite sets. By considering $ p_x $ to
describe complex phenomena, the theory leads to derive
a distinct analogous force $ f_x $ on number sets
proportional to $ (\partial p_x / \partial x)T $ at an
analogous system temperature $T$. In particular, this
leads to an understanding of the uneven distribution of
integers of random sets in terms of analogous scale
invariance and a screened inverse square force acting
on the significant digits. The theory also allows to
establish recursion relations to predict sequences of
Fibonacci numbers and to give an answer to the
interesting theoretical question of the appearance of
the Benford's law in Fibonacci numbers. A possible
relevance to prime numbers is also analyzed.",
acknowledgement = ack-nhfb,
fjournal = "Physica A: Statistical Mechanics and its
Applications",
keywords = "Benford's Law; Fibonacci numbers; Number theory; prime
numbers; Probability theory; Statistical physics and
thermodynamics",
}
@Article{Das:2003:RRE,
author = "Somnath Das and Huai Zhang",
title = "Rounding-up in reported {EPS}, behavioral thresholds,
and earnings management",
journal = "Journal of Accounting and Economics",
volume = "35",
number = "1",
pages = "31--50",
year = "2003",
DOI = "http://dx.doi.org/10.1016/S0165-4101(02)00096-4",
ISSN = "0165-4101",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165410102000964",
abstract = "Reported earnings per share (EPS) are frequently
rounded to the nearest cent. This paper provides
evidence that firms manipulate earnings so that they
can round-up and report one more cent of EPS.
Specifically, we examine the digit immediately right of
the decimal in the calculated {EPS} number expressed in
cents. Evidence is presented that firms are more likely
to round-up when managers ex ante expect rounding-up to
meet analysts forecasts, report positive profits, or
sustain recent performance. Further investigation
provides evidence that working capital accruals are
used to round-up EPS.",
acknowledgement = ack-nhfb,
keywords = "Behavioral threshold; Benford's Law; Earnings
management; Earnings per share (EPS); Rounding",
}
@Article{Engel:2003:BLE,
author = "Hans-Andreas Engel and Christoph Leuenberger",
title = "{Benford}'s law for exponential random variables",
journal = j-STAT-PROB-LETT,
volume = "63",
number = "4",
pages = "361--365",
day = "15",
month = jul,
year = "2003",
CODEN = "SPLTDC",
DOI = "http://dx.doi.org/10.1016/S0167-7152(03)00101-9",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "60E99 (60C05)",
MRnumber = "1996184 (2004d:60050)",
MRreviewer = "Ulrich M. Hirth",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715203001019",
abstract = "Benford's law assigns the probability $ \log_{10}(1 +
1 / d) $ for finding a number starting with specific
significant digit $d$. We show that exponentially
distributed numbers obey this law approximatively,
i.e., within bounds of $ 0.03$.",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Benford's Law; Exponential distribution; Significant
digit law",
}
@Article{FerreriCancho:2003:LEO,
author = "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}",
title = "Least effort and the origins of scaling in human
language",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "100",
number = "3",
pages = "788--791",
day = "4",
month = feb,
year = "2003",
CODEN = "PNASA6",
DOI = "http://dx.doi.org/10.1073/pnas.0335980100",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Tue Nov 15 09:44:47 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
keywords = "Zipf's Law",
onlinedate = "January 22, 2003",
}
@Book{Fleiss:2003:SMR,
author = "Joseph L. Fleiss and Bruce A. Levin and Myunghee Cho
Paik",
title = "Statistical Methods for Rates and Proportions",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Third",
pages = "xxvii + 760",
year = "2003",
ISBN = "0-471-52629-0 (hardcover)",
ISBN-13 = "978-0-471-52629-2 (hardcover)",
LCCN = "QA279 .F58 2003",
bibdate = "Fri Mar 22 08:46:57 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Wiley series in probability and statistics",
URL = "http://www.loc.gov/catdir/bios/wiley042/2002191005.html;
http://www.loc.gov/catdir/description/wiley034/2002191005.html;
http://www.loc.gov/catdir/toc/wiley031/2002191005.html",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
subject = "Analysis of variance; Sampling (Statistics);
Biometry",
tableofcontents = "Preface \\
Preface to the Second Edition \\
Preface to the First Edition \\
1. An Introduction to Applied Probability \\
2. Statistical Inference for a Single Proportion \\
3. Assessing Significance in a Fourfold Table \\
4. Determining Sample Sizes Needed to Detect a
Difference Between Two Proportions \\
5. How to Randomize \\
\\
6. Comparative Studies: Cross-Sectional, Naturalistic,
or Multinomial Sampling \\
\\
7. Comparative Studies: Prospective and Retrospective
Sampling \\
8. Randomized Controlled Trials \\
9. The Comparison of Proportions from Several
Independent Samples \\
10. Combining Evidence from Fourfold Tables \\
11. Logistic Regression \\
12. Poisson Regression \\
13. Analysis of Data from Matched Samples \\
14. Regression Models for Matched Samples \\
15. Analysis of Correlated Binary Data \\
16. Missing Data \\
17. Misclassification Errors: Effects, Control, and
Adjustment \\
18. The Measurement of Interrater Agreement \\
19. The Standardization of Rates \\
Appendix A. Numerical Tables \\
Appendix B. The Basic Theory of Maximum Likelihood",
}
@Article{Furusawa:2003:ZLG,
author = "Chikara Furusawa and Kunihiko Kaneko",
title = "{Zipf's Law} in Gene Expression",
journal = j-PHYS-REV-LET,
volume = "90",
number = "??",
pages = "088102",
day = "26",
month = feb,
year = "2003",
CODEN = "PRLTAO",
DOI = "http://dx.doi.org/10.1103/PhysRevLett.90.088102",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.90.088102",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Gabaix:2003:TPL,
author = "Xavier Gabaix and Parameswaran Gopikrishnan and
Vasiliki Plerou and H. Eugene Stanley",
title = "A theory of power-law distributions in financial
market fluctuations",
journal = j-NATURE,
volume = "423",
number = "6937",
pages = "267--270",
day = "15",
month = may,
year = "2003",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/nature01624",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Feb 27 06:45:03 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.nature.com/nature/journal/v423/n6937/full/nature01624.html",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Zipf's Law",
}
@InProceedings{Grekos:2003:RSC,
author = "G. Grekos and R. Giuliano-Antonini",
editor = "????",
booktitle = "{Journ{\'e}es Arithm{\'e}tiques XXIII, Graz, July
6--12, 2003}",
title = "Regular sets and conditional density: an extension of
{Benford}'s law",
publisher = "????",
address = "????",
pages = "??--??",
year = "2003",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 17:43:43 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Hassan:2003:EDA,
author = "Bassam Hassan",
title = "Examining data accuracy and authenticity with leading
digit frequency analysis",
journal = "Industrial Management + Data Systems",
volume = "103",
number = "2",
pages = "121--125",
month = "????",
year = "2003",
CODEN = "MDSD8F",
ISSN = "0263-5577 (print), 1758-5783 (electronic)",
ISSN-L = "0263-5577",
bibdate = "Fri Nov 25 11:07:59 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Book{Havil:2003:GEE,
author = "Julian Havil",
title = "{Gamma}: Exploring {Euler}'s Constant",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xxiii + 266",
year = "2003",
ISBN = "0-691-09983-9",
ISBN-13 = "978-0-691-09983-5",
LCCN = "QA41 .H23 2003",
bibdate = "Thu Sep 25 16:52:46 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Benford's Law is the subject of Section 14.2, pages
145--155.",
price = "US\$29.95",
URL = "http://www.loc.gov/catdir/description/prin031/2002192453.html",
acknowledgement = ack-nhfb,
}
@Article{Hurlimann:2003:GBL,
author = "Werner H{\"u}rlimann",
title = "A generalized {Benford} law and its application",
journal = j-ADV-APPL-STAT,
volume = "3",
number = "3",
pages = "217--228",
year = "2003",
CODEN = "????",
ISSN = "0972-3617",
ISSN-L = "0972-3617",
MRclass = "11K31 (11B73)",
MRnumber = "2034405 (2004k:11125)",
MRreviewer = "Vydas {\v{C}}ekanavi{\v{c}}ius",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Advances and Applications in Statistics",
}
@Article{Ioannides:2003:ZLC,
author = "Yannis M. Ioannides and Henry G. Overman",
title = "{Zipf}'s law for cities: an empirical examination",
journal = j-REG-SCI-URBAN-ECON,
volume = "33",
number = "2",
pages = "127--137",
day = "1",
month = mar,
year = "2003",
CODEN = "RSUEDM",
DOI = "http://dx.doi.org/10.1016/S0166-0462(02)00006-6",
ISSN = "0166-0462 (print), 1879-2308 (electronic)",
ISSN-L = "0166-0462",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0166046202000066",
acknowledgement = ack-nhfb,
fjournal = "Regional Science and Urban Economics",
journal-URL = "http://www.sciencedirect.com/science/journal/01660462",
keywords = "Zipf's Law",
}
@Article{Kreiner:2003:NBL,
author = "W. A. Kreiner",
title = "On the {Newcomb--Benford} law",
journal = j-Z-NATURFORSCH,
volume = "58a",
number = "11",
pages = "618--622",
month = "????",
year = "2003",
CODEN = "ZNTFA2",
ISSN = "0372-9516",
ISSN-L = "0372-9516",
bibdate = "Sat Feb 16 18:19:41 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.znaturforsch.com/aa/v58a/s58a0618.pdf",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Naturforschung}",
}
@InCollection{Kumar:2003:BLA,
author = "Kuldeep Kumar and Sukanto Bhattacharya",
editor = "Cheng-Few Lee",
booktitle = "Advances in Financial Planning and Forecasting",
title = "{Benford}'s law and its application in financial fraud
detection",
volume = "11",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "57--70",
year = "2003",
ISBN = "0-7623-1016-2",
ISBN-13 = "978-0-7623-1016-6",
ISSN = "1046-5847",
LCCN = "????",
bibdate = "Wed Nov 23 16:45:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
bookpages = "ix + 177",
}
@Article{Lanza:2003:FSP,
author = "Richard B. Lanza",
title = "Fear Not the Software: Proactively Detecting
Occupational Fraud Using Computer Audit Reports",
journal = "Fraud Magazine",
volume = "??",
number = "??",
pages = "??--??",
month = sep # "\slash " # feb,
year = "2003",
ISSN = "1553-6645",
ISSN-L = "1553-6645",
bibdate = "Sun Feb 17 08:14:47 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.fraud-magazine.com/article.aspx?id=4294967868",
acknowledgement = ack-nhfb,
fjournal = "Fraud Magazine. {A} Publication of the Association of
Certified Fraud Examiners",
keywords = "Benford's Law",
}
@InProceedings{Manaris:2003:EMZ,
author = "Bill Manaris and Dallas Vaughan and Christopher Wagner
and Juan Romero and Robert B. Davis",
title = "Evolutionary Music and the {Zipf--Mandelbrot Law}:
Developing Fitness Functions for Pleasant Music",
crossref = "Raidl:2003:AEC",
pages = "522--534",
year = "2003",
bibdate = "Mon Feb 18 10:49:54 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{McAllister:2003:ARE,
author = "James W. McAllister",
title = "Algorithmic randomness in empirical data",
journal = j-STUD-HIST-PHILOS-SCI,
volume = "34",
number = "3",
pages = "633--646",
month = sep,
year = "2003",
CODEN = "SHPSB5",
DOI = "http://dx.doi.org/10.1016/S0039-3681(03)00047-5",
ISSN = "0039-3681 (print), 1879-2510 (electronic)",
ISSN-L = "0039-3681",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/shps-a.bib;
http://www.sciencedirect.com/science/journal/00393681",
note = "See replies
\cite{Twardy:2005:EDS,McAllister:2005:ACE}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0039368103000475",
abstract = "According to a traditional view, scientific laws and
theories constitute algorithmic compressions of
empirical data sets collected from observations and
measurements. This article defends the thesis that, to
the contrary, empirical data sets are algorithmically
incompressible. The reason is that individual data
points are determined partly by perturbations, or
causal factors that cannot be reduced to any pattern.
If empirical data sets are incompressible, then they
exhibit maximal algorithmic complexity, maximal entropy
and zero redundancy. They are therefore maximally
efficient carriers of information about the world.
Since, on algorithmic information theory, a string is
algorithmically random just if it is incompressible,
the thesis entails that empirical data sets consist of
algorithmically random strings of digits. Rather than
constituting compressions of empirical data, scientific
laws and theories pick out patterns that data sets
exhibit with a certain noise.",
acknowledgement = ack-nhfb,
fjournal = "Studies in History and Philosophy of Science Part
{A}",
journal-URL = "http://www.sciencedirect.com/science/journal/00393681",
keywords = "Algorithmic randomness; Benford's Law; Compression;
Empirical data; Information; Law; Pattern",
}
@Article{Mitzenmacher:2003:BHG,
author = "Michael Mitzenmacher",
title = "A Brief History of Generative Models for Power Law and
Lognormal Distributions",
journal = j-INTERNET-MATH,
volume = "1",
number = "2",
pages = "226--251",
month = dec,
year = "2003",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/15427951.2004.10129088",
ISSN = "1542-7951 (print), 1944-9488 (electronic)",
ISSN-L = "1542-7951",
bibdate = "Thu Nov 24 13:38:13 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/euclid.im/1089229510;
http://www.eecs.harvard.edu/~michaelm/CS223/powerlaw.pdf;
http://www.tandfonline.com/toc/uinm20/1/2",
acknowledgement = ack-nhfb,
ajournal = "Internet Math.",
fjournal = "Internet Mathematics",
journal-URL = "http://projecteuclid.org/info/euclid.im",
keywords = "Fibonacci sequence; lognormal distribution; monkeys
typing randomly; Pareto distribution; power-law
distribution; Yule distribution; Zipf's Law",
remark = "This is a survey article with a six-page bibliography
of earlier work, and a clear description of the
differences between lognormal and power-law
distributions, which otherwise look similar on log-log
plots. Lognormal distributions have finite means and
moments, while power-law distributions may have
infinite means and/or moments, depending on the
exponent. The preprint at author's Web site (last URL)
contains additional material on the acrimonious debate
between Beno{\^\i}t Mandelbrot and Herbert A. Simon
(see \cite{Mandelbrot:1959:NCS,Simon:1955:CSD}, and
other references in Mitzenmacher's paper) on the
derivation and modeling of Zipf's Law distributions.",
}
@PhdThesis{Muller:2003:AZP,
author = "Mathias M{\"u}ller",
title = "{Anwendungsm{\"o}glichkeiten der Ziffernanalyse in der
Pr{\"u}fungspraxis mit Schwerpunkt auf Benford's Law}.
({German}) [Applications of the digit analysis in the
audit practice with a focus on {Benford's Law}]",
type = "{Diplomarbeit}",
school = "Wirtschaftsuniversit{\"a}t Wien",
address = "Wien, Austria",
pages = "v + 75",
month = "????",
year = "2003",
bibdate = "Sat Feb 16 18:44:50 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://permalink.obvsg.at/wuw/AC03895842",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Naldi:2003:CIZ,
author = "M. Naldi",
title = "Concentration indices and {Zipf}'s law",
journal = j-ECONOM-LETT,
volume = "78",
number = "3",
pages = "329--334",
month = mar,
year = "2003",
CODEN = "ECLEDS",
DOI = "http://dx.doi.org/10.1016/S0165-1765(02)00251-3",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
MRclass = "91B82",
MRnumber = "1959355",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165176502002513",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
keywords = "Zipf's Law",
}
@Article{Nguyen:2003:DPL,
author = "H. T. Nguyen and V. Kreinovich and L. Longpre",
title = "Dirty pages of logarithm tables, lifetime of the
universe, and subjective (fuzzy) probabilities on
finite and infinite intervals",
journal = j-IEEE-TRANS-FUZZY-SYSTEMS,
volume = "1",
pages = "67--73",
year = "2003",
CODEN = "IEFSEV",
DOI = "http://dx.doi.org/10.1109/FUZZ.2003.1209339",
ISSN = "1063-6706 (print), 1941-0034 (electronic)",
ISSN-L = "1063-6706",
bibdate = "Sat Feb 16 18:51:15 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "The 12th IEE International Conference on Fuzzy
Systems. FUZZ'03",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Fuzzy Systems",
xxnote = "Is this the listed journal, or a conference paper??",
}
@Article{Peter:2003:ADE,
author = "Manfred Peter",
title = "The asymptotic distribution of elements in automatic
sequences",
journal = j-THEOR-COMP-SCI,
volume = "301",
number = "1 3",
pages = "285--312",
year = "2003",
CODEN = "TCSCDI",
DOI = "http://dx.doi.org/10.1016/S0304-3975(02)00587-X",
ISSN = "0304-3975",
ISSN-L = "0304-3975",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S030439750200587X",
abstract = "In an automatic sequence an element need not have an
asymptotic density. In this paper a necessary and
sufficient criterion is proved for the existence of the
asymptotic density of a given element. If it does not
exist the asymptotic distribution of the element can be
described in terms of a function H whose graph is
self-similar. An algorithm is given to decide whether H
is piecewise continuously differentiable, and in this
case it can be computed effectively. Finally, it is
shown that the H -density of an element in an automatic
sequence always exists and equals its logarithmic
density.",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
keywords = "Asymptotics; Automata; Benford's Law; Density;
H{\"o}lder mean; Oscillating sum; Self-similarity",
}
@Article{Quick:2003:BLD,
author = "Reiner Quick and Matthias Wolz",
title = "{Benford's Law in deutschen Rechnungslegungsdaten}.
({German}) [{Benford's Law} in {German} accounting
data]",
journal = "Betriebswirtschaftliche Forschung und Praxis",
volume = "55",
number = "2",
pages = "208--224",
month = "????",
year = "2003",
CODEN = "????",
ISSN = "0340-5370",
ISSN-L = "0340-5370",
bibdate = "Sat Dec 10 12:01:20 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
remark = "Betriebswirtschaftliche Forschung und Praxis ==
Business Research and Practice.",
}
@Article{Reed:2003:PLI,
author = "William J. Reed",
title = "The {Pareto} law of incomes---an explanation and an
extension",
journal = j-PHYSICA-A,
volume = "319",
number = "1--4",
pages = "469--486",
year = "2003",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(02)01507-8",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "91B70",
MRnumber = "1965596",
bibdate = "Mon Feb 18 17:05:26 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
}
@Article{Rose:2003:TEF,
author = "Anna M. Rose and Jacob M. Rose",
title = "Turn {Excel} into a financial sleuth: an easy-to-use
digital analysis tool can red-flag irregularities",
journal = j-J-ACCOUNTANCY,
volume = "196",
number = "2",
pages = "58--??",
month = aug,
year = "2003",
CODEN = "JACYAD",
ISSN = "0021-8448 (print), 1945-0729 (electronic)",
ISSN-L = "0021-8448",
bibdate = "Sat Feb 16 19:07:02 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.journalofaccountancy.com/Issues/2003/Aug/TurnExcelIntoAFinancialSleuth",
acknowledgement = ack-nhfb,
fjournal = "Journal of Accountancy",
journal-URL = "http://www.journalofaccountancy.com/",
}
@Article{Sinai:2003:SP,
author = "Ya. G. Sinai",
title = "Statistical $ (3 x + 1) $ problem",
journal = j-COMM-PURE-APPL-MATH,
volume = "56",
number = "??",
pages = "1016--1028",
month = "????",
year = "2003",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
bibdate = "Mon Nov 21 07:52:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Dedicated to the memory of J{\"u}rgen K. Moser.",
acknowledgement = ack-nhfb,
fjournal = "Communications on Pure and Applied Mathematics (New
York)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
}
@InProceedings{Swanson:2003:DPF,
author = "David Swanson and Moon Jung Cho and John Eltinge",
editor = "????",
booktitle = "Proceedings of the Survey Research Section",
title = "Detecting possibly fraudulent or error-prone survey
data using {Benford's Law}",
publisher = "American Statistical Association",
address = "Washington, DC, USA",
pages = "4172--4177",
year = "2003",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Wed Nov 16 10:21:39 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.amstat.org/sections/srms/proceedings/y2003/Files/JSM2003-000205.pdf.",
acknowledgement = ack-nhfb,
}
@Article{Wales:2003:IWI,
author = "Elspeth Wales",
title = "Is it Worth Investing in Software to Combat Fraud?",
journal = "Computer Fraud & Security",
volume = "2003",
number = "5",
pages = "6--8",
year = "2003",
DOI = "http://dx.doi.org/10.1016/S1361-3723(03)05009-7",
ISSN = "1361-3723",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1361372303050097",
abstract = "Despite the tendency for businesses to keep fraud to
themselves, the consensus is that the problem is
becoming worse. On the plus side though software
solutions that can detect potential fraudulent activity
are evolving in their scope and ability to
automatically track transactions in real-time.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@InCollection{Warren:2003:DLD,
author = "Henry S. Warren",
title = "The distribution of leading digits",
crossref = "Warren:2003:HD",
chapter = "15.3",
pages = "264--267",
year = "2003",
bibdate = "Fri Mar 16 08:02:56 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Wu:2003:IPD,
author = "Shuo-Jye Wu and Chun-Tao Chang",
title = "Inference in the {Pareto} distribution based on
progressive {Type II} censoring with random removals",
journal = j-J-APPL-STAT,
volume = "30",
number = "2",
pages = "163--172",
month = "????",
year = "2003",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Tue Dec 16 15:40:48 MST 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
}
@Article{Wu:2003:PDC,
author = "Wei Biao Wu and Chinya V. Ravishankar",
title = "The performance of difference coding for sets and
relational tables",
journal = j-J-ACM,
volume = "50",
number = "5",
pages = "665--693",
month = sep,
year = "2003",
CODEN = "JACOAH",
DOI = "http://doi.acm.org/10.1145/876638.876641",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Mon Sep 8 17:55:23 MDT 2003",
bibsource = "http://portal.acm.org/; http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "We characterize the performance of difference coding
for compressing sets and database relations through an
analysis of the problem of estimating the number of
bits needed for storing the spacings between values in
sets of integers. We provide analytical expressions for
estimating the effectiveness of difference coding when
the elements of the sets or the attribute fields in
database tuples are drawn from the uniform and Zipf
distributions. We also examine the case where a
uniformly distributed domain is combined with a Zipf
distribution, and with an arbitrary distribution. We
present limit theorems for most cases, and
probabilistic convergence results in other cases. We
also examine the effects of attribute domain reordering
on the compression ratio. Our simulations show
excellent agreement with theory.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Aoyama:2004:KDP,
author = "Hideaki Aoyama and Yoshi Fujiwara and Wataru Souma",
title = "Kinematics and dynamics of {Pareto--Zipf}'s law and
{Gibrat}'s law",
journal = j-PHYSICA-A,
volume = "344",
number = "1--2",
pages = "117--121",
day = "1",
month = dec,
year = "2004",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2004.06.099",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437104009185",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@TechReport{Berger:2004:DDU,
author = "A. Berger",
title = "Dynamics and digits: on the ubiquity of {Benford's
Law}",
type = "Preprint",
institution = "Institute of Mechanics, Vienna University of
Technology",
address = "Vienna, Austria",
pages = "3",
day = "19",
month = nov,
year = "2004",
bibdate = "Sat Feb 16 17:20:58 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.math.leidenuniv.nl/~verduyn/EQUADIFF03/MS14/berger_eqdiff03.pdf",
acknowledgement = ack-nhfb,
}
@Article{Challet:2004:BPD,
author = "Damien Challet and Andrea Lombardoni",
title = "Bug propagation and debugging in asymmetric software
structures",
journal = j-PHYS-REV-E,
volume = "70",
number = "4",
pages = "046109",
month = oct,
year = "2004",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.70.046109",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Thu Feb 28 08:15:07 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.70.046109;
http://pre.aps.org/abstract/PRE/v70/i4/e046109",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
issue = "4",
journal-URL = "http://pre.aps.org/browse",
keywords = "Linux; Unix; Zipf's Law",
pagecount = "5",
}
@Article{Chen:2004:MFM,
author = "Yanguang Chen and Yixing Zhou",
title = "Multi-fractal measures of city-size distributions
based on the three-parameter {Zipf} model",
journal = j-CHAOS-SOLITONS-FRACTALS,
volume = "22",
number = "4",
pages = "793--805",
day = "1",
month = nov,
year = "2004",
CODEN = "CSFOEH",
DOI = "http://dx.doi.org/10.1016/j.chaos.2004.02.059",
ISSN = "0960-0779 (print), 1873-2887 (electronic)",
ISSN-L = "0960-0779",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0960077904001031",
acknowledgement = ack-nhfb,
fjournal = "Chaos, Solitons \& Fractals",
keywords = "Zipf's Law",
}
@Article{Cong:2004:WTP,
author = "Lin Cong and Zhipeng Li",
title = "On {Wilson}'s theorem and {Polignac} conjecture",
journal = "ArXiv e-prints",
day = "2",
month = aug,
year = "2004",
bibdate = "Mon Feb 18 07:03:53 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/math.NT/0408018",
abstract = "We introduce Wilson's theorem and Clement's result and
present a necessary and sufficient condition for $p$
and $ p + 2 k $ to be primes where $k$ is a positive
integer. By using Simiov's Theorem, we derive an
improved version of Clement's result and
characterizations of Polignac twin primes which
parallel previous characterizations.",
acknowledgement = ack-nhfb,
}
@TechReport{Diekmann:2004:DEE,
author = "Andreas Diekmann",
title = "{Datenf{\"a}lschung. Ergebnisse aus Experimenten mit
der Benford Verteilung}. ({German}) [{Data}
falsification. {Results} from experiments with the
{Benford} distribution]",
type = "Report",
institution = "ETH Z{\"u}rich",
address = "Z{\"u}rich, Switzerland",
year = "2004",
bibdate = "Fri Nov 18 12:09:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@TechReport{Diekmann:2004:FDU,
author = "Andreas Diekmann",
title = "Not the First Digit! {Using} {Benford's Law} to Detect
Fraudulent Scientific Data",
type = "Report",
institution = "ETH Z{\"u}rich",
address = "Z{\"u}rich, Switzerland",
pages = "26",
month = oct,
year = "2004",
bibdate = "Sat Dec 10 11:12:29 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://rfe.cs.oswego.edu/eps/othr/papers/0507/0507001.pdf",
abstract = "Digits in statistical data produced by natural or
social processes are often distributed in a manner
described by ``Benford's law''. Recently, a test
against this distribution was used to identify
fraudulent accounting data. This test is based on the
supposition that real data follow the Benford
distribution while fabricated data do not. Is it
possible to apply Benford tests to detect fabricated or
falsified scientific data as well as fraudulent
financial data? We approached this question in two
ways. First, we examined the use of the Benford
distribution as a standard by checking digit
frequencies in published statistical estimates. Second,
we conducted experiments in which subjects were asked
to fabricate statistical estimates (regression
coefficients). These experimental data were scrutinized
for possible deviations from the Benford distribution.
There were two main findings. First, the digits of the
published regression coefficients were approximately
Benford distributed. Second, the experimental results
yielded new insights into the strengths and weaknesses
of Benford tests. At least in the case of regression
coefficients, there were indications that checks for
digit-preference anomalies should focus less on the
first and more on the second and higher-digits",
acknowledgement = ack-nhfb,
}
@Article{Durtschi:2004:EUB,
author = "C. Durtschi and W. Hillison and C. Pacini",
title = "The Effective Use of {Benford's Law} to Assist in
Detecting Fraud in Accounting Data",
journal = j-J-FORENSIC-ACCOUNT,
volume = "5",
number = "1",
pages = "17--34",
month = "????",
year = "2004",
CODEN = "????",
ISSN = "1524-5586",
bibdate = "Sun Nov 13 11:35:18 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Forensic Accounting",
}
@Article{Fontanari:2004:SNM,
author = "J. F. Fontanari and L. I. Perlovsky",
title = "Solvable null model for the distribution of word
frequencies",
journal = j-PHYS-REV-E,
volume = "70",
number = "??",
pages = "042901",
day = "25",
month = oct,
year = "2004",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.70.042901",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.70.042901",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Fujiwara:2004:DPZ,
author = "Yoshi Fujiwara and Corrado {Di Guilmi} and Hideaki
Aoyama and Mauro Gallegati and Wataru Souma",
title = "Do {Pareto--Zipf} and {Gibrat} laws hold true? {An}
analysis with {European} firms",
journal = j-PHYSICA-A,
volume = "335",
number = "1--2",
pages = "197--216",
day = "1",
month = apr,
year = "2004",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2003.12.015",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437103011294",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Article{Fujiwara:2004:GPZ,
author = "Yoshi Fujiwara and Hideaki Aoyama and Corrado {Di
Guilmi} and Wataru Souma and Mauro Gallegati",
title = "{Gibrat} and {Pareto--Zipf} revisited with {European}
firms",
journal = j-PHYSICA-A,
volume = "344",
number = "1--2",
pages = "112--116",
day = "1",
month = dec,
year = "2004",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2004.06.098",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437104009173",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Article{Fujiwara:2004:ZLF,
author = "Yoshi Fujiwara",
title = "{Zipf} law in firms bankruptcy",
journal = j-PHYSICA-A,
volume = "337",
number = "1--2",
pages = "219--230",
day = "1",
month = jun,
year = "2004",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2004.01.037",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "91B38",
MRnumber = "2092316",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437104001165",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Article{Geyer:2004:DFD,
author = "Christina Lynn Geyer and Patricia Pepple Williamson",
title = "Detecting fraud in data sets using {Benford's Law}",
journal = j-COMM-STAT,
volume = "B33",
number = "1",
pages = "229--246",
month = "????",
year = "2004",
CODEN = "CSSCDB",
DOI = "http://dx.doi.org/10.1081/SAC-120028442",
ISSN = "0361-0918",
ISSN-L = "0361-0918",
MRclass = "62-07",
MRnumber = "2044866",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Comm. Statist. Simulation Comput.",
fjournal = "Communications in Statistics. Simulation and
Computation",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Hurlimann:2004:IPB,
author = "Werner H{\"u}rlimann",
title = "Integer powers and {Benford}'s law",
journal = j-INT-J-PURE-APPL-MATH,
volume = "11",
number = "1",
pages = "39--46",
year = "2004",
CODEN = "????",
ISSN = "1311-8080",
ISSN-L = "1314-3395",
MRclass = "62E15 (11B83 11K31 62E20)",
MRnumber = "2033394 (2005c:62030)",
MRreviewer = "I. N. Volodin",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Pure and Applied
Mathematics",
journal-URL = "http://ijpam.eu/",
}
@Article{Ismail:2004:SES,
author = "Sanaa Isma{\"\i}l",
title = "A Simple Estimator for the Shape Parameter of the
{Pareto} Distribution with Economics and Medical
Applications",
journal = j-J-APPL-STAT,
volume = "31",
number = "1",
pages = "3--13",
month = jan,
year = "2004",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Sat Dec 4 12:10:37 MST 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
}
@Article{Janvresse:2004:UDB,
author = "{\'E}lise Janvresse and Thierry de la Rue",
title = "From uniform distributions to {Benford}'s law",
journal = j-J-APPL-PROBAB,
volume = "41",
number = "4",
pages = "1203--1210",
year = "2004",
CODEN = "JPRBAM",
DOI = "http://dx.doi.org/10.1239/jap/1101840566",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
MRclass = "60J20 (60J10)",
MRnumber = "2122815 (2006b:60161)",
MRreviewer = "Michael Drmota",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/getRecord?id=euclid.jap/1101840566;
http://www.jstor.org/stable/4141393;
https://www.univ-rouen.fr/LMRS/Persopage/Delarue/Publis/PDF/uniform_distribution_to_Benford_law.pdf",
abstract = "We provide a new, probabilistic explanation for the
appearance of Benford's law in everyday-life numbers,
by showing that it arises naturally when we consider
mixtures of uniform distributions. Then we connect our
result to a result of Flehinger, for which we provide a
shorter proof, and the speed of convergence.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Probability",
journal-URL = "http://www.jstor.org/journals/00219002.html;
http://projecteuclid.org/euclid.jap/",
}
@TechReport{Kollath-Romano:2004:DSD,
author = "P. Kollath-Romano",
title = "On the distribution of significant digits in numbers",
type = "Preprint",
institution = "Rensselaer Polytechnic Institute",
address = "Troy, NY, USA",
year = "2004",
bibdate = "Sat Feb 16 18:15:19 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Kotz:2004:FDP,
author = "Samuel Kotz and N. Balakrishnan and Campbell B. Read
and Brani Vidakovic",
editor = "Samuel Kotz and N. Balakrishnan and Campbell B. Read
and Brani Vidakovic",
booktitle = "Encyclopedia of Statistical Sciences",
title = "First-Digit Problem",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Second",
pages = "??--??",
year = "2004",
DOI = "http://dx.doi.org/10.1002/0471667196.ess0783.pub2",
ISBN = "0-471-66719-6 (e-book)",
ISBN-13 = "978-0-471-66719-3 (e-book)",
bibdate = "Sun Feb 24 10:49:25 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Kristiansen:2004:BTZ,
author = "Kai de Lange Kristiansen and Geir Helgesen and Arne T.
Skjeltorp",
title = "Braid theory and {Zipf} relation used in dynamics of
magnetic microparticles",
journal = j-ECONOM-LETT,
volume = "30",
number = "1",
pages = "2387--2388",
day = "1",
month = may,
year = "2004",
CODEN = "ECLEDS",
DOI = "http://dx.doi.org/10.1016/j.jmmm.2003.12.1288",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0304885303019127",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
keywords = "Zipf's Law",
}
@Article{Kristiansen:2004:EOZ,
author = "Kai de Lange Kristiansen and Geir Helgesen and Arne T.
Skjeltorp",
title = "Experimental observation of {Zipf--Mandelbrot}
relation",
journal = j-PHYSICA-A,
volume = "335",
number = "3--4",
pages = "413--420",
day = "15",
month = apr,
year = "2004",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2003.12.024",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "82D10 (76T99 82-05)",
MRnumber = "2044153",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437103011804",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Article{Kulikova:2004:OSS,
author = "A. A. Kulikova and Yu. V. Prokhorov",
title = "One-sided stable distributions and {Benford}'s law",
journal = "Teor. Veroyatn. Primen.",
volume = "49",
number = "1",
pages = "178--184",
year = "2004",
CODEN = "????",
DOI = "http://dx.doi.org/10.1137/S0040585X97980944",
ISSN = "0040-361X",
ISSN-L = "0040-361X",
MRclass = "60E07 (60F05)",
MRnumber = "2141338 (2005m:60028)",
MRreviewer = "S{\'a}ndor Cs{\"o}rg{\H{o}}",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoriya
Veroyatnoste{\u\i} i ee Primeneniya",
}
@Article{Lanza:2004:CBS,
author = "Richard B. Lanza",
title = "Comparing Best Software for Fraud Examinations: Fraud
Data Interrogation Tools",
journal = "Fraud Magazine",
volume = "??",
number = "??",
pages = "??--??",
month = nov # "\slash" # dec,
year = "2004",
ISSN = "1553-6645",
ISSN-L = "1553-6645",
bibdate = "Sun Feb 17 08:17:02 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.fraud-magazine.com/article.aspx?id=4294967837",
acknowledgement = ack-nhfb,
fjournal = "Fraud Magazine. {A} Publication of the Association of
Certified Fraud Examiners",
keywords = "Benford's Law",
}
@Article{Lehner:2004:DVG,
author = "B. Lehner and P. Doll",
title = "Development and validation of a global database of
lakes",
journal = j-J-HYDROL,
volume = "296",
number = "1--4",
pages = "1--22",
day = "20",
month = aug,
year = "2004",
CODEN = "JHYDA7",
DOI = "http://dx.doi.org/10.1016/j.jhydrol.2004.03.028",
ISSN = "0022-1694 (print), 1879-2707 (electronic)",
ISSN-L = "0022-1694",
bibdate = "Fri Mar 22 08:54:27 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022169404001404",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
fjournal = "Journal of Hydrology",
keywords = "Benford's Law",
}
@Article{Li:2004:DBL,
author = "Zhi-peng Li and Lin Cong and Hua-jia Wang",
title = "Discussion on {Benford's Law} and its Application",
journal = "ArXiv e-prints",
pages = "1--13",
year = "2004",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 16:17:04 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2004math......8057L;
http://arxiv.org/abs/math/0408057",
abstract = "The probability that a number in many naturally
occurring tables of numerical data has first
significant digit $d$ is predicted by Benford's Law $
{\rm Prob} (d) = \log_{10} (1 + {\displaystyle {1 \over
d}}), d = 1, 2, \ldots, 9 $. Illustrations of Benford's
Law from both theoretical and real-life sources on both
science and social science areas are shown in detail
with some novel ideas and generalizations developed
solely by the authors of this paper. Three tests,
Chi-Square test, total variation distance, and maximum
deviations are adopted to examine the fitness of the
datasets to Benford's distribution. Finally,
applications of Benford's Law are summarized and
explored to reveal the power of this mathematical
principle.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "math/0408057",
}
@Article{Lindsay:2004:DFD,
author = "D. H. Lindsay and P. S. Foote and A. Campbell and D.
R. Reilly",
title = "Detecting fraud in the data using automatic
intervention detection",
journal = "Fraud Magazine",
volume = "??",
number = "??",
pages = "??--??",
month = jan # "\slash " # feb,
year = "2004",
ISSN = "1553-6645",
ISSN-L = "1553-6645",
bibdate = "Sat Feb 16 18:32:22 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Fraud Magazine. {A} Publication of the Association of
Certified Fraud Examiners",
}
@TechReport{Miller:2004:STB,
author = "Steven J. Miller",
title = "Some thoughts on {Benford}'s law",
type = "Preprint",
institution = "Williams College",
address = "Williamstown, MA 01267 USA",
year = "2004",
bibdate = "Sat Feb 16 18:43:46 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.williams.edu/go/math/sjmiller/public_html/BrownClasses/1/BenfordTreatise.pdf",
acknowledgement = ack-nhfb,
remark = "URL not found on 17 February 2013; perhaps in ReCALL
2004 proceedings",
}
@Article{Molchanov:2004:BEL,
author = "Stanislav Molchanov and Xian Wang",
title = "On the {Benford}'s empirical law",
journal = "Random Oper. Stochastic Equations",
volume = "12",
number = "3",
pages = "201--210",
year = "2004",
CODEN = "????",
DOI = "http://dx.doi.org/10.1163/1569397042222495",
ISSN = "0926-6364 (print), 1569-397X (electronic)",
ISSN-L = "0926-6364",
MRclass = "11K16 (11B39 60B15)",
MRnumber = "2084074 (2005h:11162)",
MRreviewer = "A. N. Philippou",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Random Operators and Stochastic Equations",
}
@Article{Nabeshima:2004:ZLP,
author = "Terutaka Nabeshima and Yukio-Pegio Gunji",
title = "{Zipf}'s law in phonograms and {Weibull} distribution
in ideograms: comparison of {English} with {Japanese}",
journal = j-BIOSYSTEMS,
volume = "73",
number = "2",
pages = "131--139",
day = "20",
month = feb,
year = "2004",
CODEN = "BSYMBO",
DOI = "http://dx.doi.org/10.1016/j.biosystems.2003.11.002",
ISSN = "0303-2647 (print), 1872-8324 (electronic)",
ISSN-L = "0303-2647",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0303264703002260",
acknowledgement = ack-nhfb,
fjournal = "Biosystems (A6E)",
keywords = "Zipf's Law",
}
@Article{Nguyen:2004:DPL,
author = "Hung T. Nguyen and Vladik Kreinovich and Luc
Longpr{\'e}",
title = "Dirty Pages of Logarithm Tables, Lifetime of the
Universe, and (Subjective) Probabilities on Finite and
Infinite Intervals",
journal = j-RELIABLE-COMPUTING,
volume = "10",
number = "2",
pages = "83--106",
month = apr,
year = "2004",
CODEN = "RCOMF8",
DOI = "http://dx.doi.org/10.1023/B:REOM.0000015848.19449.12",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Mon Feb 6 07:42:05 MST 2012",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=10&issue=2;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/rc.bib",
URL = "http://link.springer.com/article/10.1023/B%3AREOM.0000015848.19449.12/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=2&spage=83;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=2&spage=83-106",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@InProceedings{Pericchi:2004:LNB,
author = "Luis R{\'a}ul Pericchi and David Torres",
editor = "????",
booktitle = "{Third Universidad Simon Bolivar Seminar on
Statistical Analyses of the Venezuelan Recall
Referendum}",
title = "La {Ley de Newcomb--Benford} y sus aplicaciones al
Referendum Revocatorio en {Venezuela}. ({Spanish}) [The
{Newcomb--Benford Law} and its applications to the
recall referendum in {Venezuela}]",
publisher = "????",
address = "????",
pages = "1--7",
day = "1",
month = oct,
year = "2004",
bibdate = "Fri Feb 15 18:25:14 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Reporte T{\'e}cnico no-definitivo 2a. Presented on
September 23, 2004.",
URL = "http://esdata.info/pdf/pericchi-torres.pdf;
https://sites.google.com/a/upr.edu/probability-and-statistics/home/techical-reports",
acknowledgement = ack-nhfb,
language = "Spanish",
}
@TechReport{Posch:2004:BBH,
author = "Peter N. Posch",
title = "{Benford} or not-{Benford}? {How} to test for the
first digit law",
type = "Working paper.",
institution = "Department of Finance, University of Ulm",
address = "Ulm, Germany",
year = "2004",
bibdate = "Sat Feb 16 19:05:45 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Posch:2004:SSD,
author = "Peter N. Posch",
title = "A survey on sequences and distribution functions
satisfying {Benford}'s law",
type = "Working paper.",
institution = "Department of Finance, University of Ulm",
address = "Ulm, Germany",
day = "25",
month = oct,
year = "2004",
bibdate = "Sat Feb 16 19:05:45 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.posch.org/paper/posch_benforddist.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Posch:2004:ZFB,
author = "Peter N. Posch",
title = "{Ziffernanalyse in der F{\"a}lschungsaufsp{\"u}rung.
Benford's Gesetz und Steuererkl{\"a}rungen in Theorie
und Praxis}. ({German}) [Digit analysis in fake
tracing. {Benford's Law} and tax returns in theory and
practice]",
type = "Arbeitspapier",
institution = "Abteilung Finanzwirtschaft, University Ulm",
address = "Ulm, Germany",
month = oct,
year = "2004",
bibdate = "Sat Feb 16 19:03:27 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Pustet:2004:ZHH,
author = "Regina Pustet",
title = "{Zipf} and his heirs",
journal = j-LANG-SCI,
volume = "26",
number = "1",
pages = "1--25",
day = "1",
month = jan,
year = "2004",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/S0388-0001(03)00018-4",
ISSN = "0388-0001 (print), 1873-5746 (electronic)",
ISSN-L = "0388-0001",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0388000103000184",
abstract = "During the first half of this century, George Kingsley
Zipf devised a comprehensive model of language mainly
on the empirical basis of frequency counts in
discourse. Although Zipf is remembered particularly for
establishing the general formula the higher the
discourse frequency of a linguistic item, the shorter
it will be, his model is complex enough to merit
re-evaluation especially in the light of more recent
findings of discourse-based models of language and
grammaticalization theory.",
acknowledgement = ack-nhfb,
fjournal = "Language Sciences",
journal-URL = "http://www.sciencedirect.com/science/journal/03880001",
keywords = "Benford's Law; Diachronic development of language;
Discourse analysis; George Kingsley Zipf; Usage-based
models of language; Word frequency; Zipf's Law",
}
@Article{Rawlings:2004:EBP,
author = "Philip K. Rawlings and David Reguera and Howard
Reiss",
title = "Entropic basis of the {Pareto} law",
journal = j-PHYSICA-A,
volume = "343",
number = "1--4",
pages = "643--652",
year = "2004",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2004.06.152",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "91B26 (91B82)",
MRnumber = "2094418 (2005e:91065)",
bibdate = "Mon Feb 18 17:05:26 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
}
@Article{Rodriguez:2004:FSD,
author = "Ricardo J. Rodriguez",
title = "First Significant Digit Patterns From Mixtures of
Uniform Distributions",
journal = j-AMER-STAT,
volume = "58",
number = "1",
pages = "64--71",
month = feb,
year = "2004",
CODEN = "ASTAAJ",
DOI = "http://dx.doi.org/10.1198/0003130042782",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Feb 20 06:14:28 MST 2004",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://oberon.ingentaselect.com/cgi-bin/linker?ini=asa&reqidx=/cw/asa/00031305/v58n1/s13/p64",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
keywords = "Benford's Law",
}
@TechReport{Saville:2004:SWN,
author = "A. Saville",
title = "Sorry, wrong number. {How} accounting data are wrong
and how the numbers can be fixed",
type = "Preprint",
institution = "????",
address = "????",
month = "????",
year = "2004",
bibdate = "Sat Feb 16 19:11:00 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Sigurd:2004:WLS,
author = "Bengt Sigurd and Mats Eeg-Olofsson and Joost {Van
Weijer}",
title = "Word length, sentence length and frequency --- {Zipf}
revisited",
journal = j-STUD-LINGUISTICA,
volume = "58",
number = "1",
pages = "37--52",
year = "2004",
DOI = "http://dx.doi.org/10.1111/j.0039-3193.2004.00109.x",
ISSN = "0039-3193 (print), 1467-9582 (electronic)",
ISSN-L = "0039-3193",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Studia Linguistica",
}
@Article{Skousen:2004:AUP,
author = "Christopher J. Skousen and Liming Guan and T. Sterling
Wetzel",
title = "Anomalies and Unusual Patterns in Reported Earnings:
{Japanese} Managers Round Earnings",
journal = j-J-INT-FINANC-MANAG-ACCOUNT,
volume = "15",
number = "3",
pages = "212--234",
month = oct,
year = "2004",
CODEN = "????",
DOI = "http://dx.doi.org/10.1111/j.1467-646X.2004.00108.x",
ISSN = "0954-1314 (print), 1467-646X (electronic)",
ISSN-L = "0954-1314",
bibdate = "Fri Nov 25 11:11:38 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of International Financial Management and
Accounting",
}
@Book{Tijms:2004:UPC,
author = "Henk C. Tijms",
title = "Understanding probability: chance rules in everyday
life",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "x + 380",
year = "2004",
ISBN = "0-521-83329-9 (hardcover), 0-521-54036-4 (paperback)",
ISBN-13 = "978-0-521-83329-5 (hardcover), 978-0-521-54036-0
(paperback)",
LCCN = "QA273 .T48 2004",
bibdate = "Mon Feb 18 06:48:08 MST 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
subject = "Probabilities; Mathematical analysis; Chance;
Wahrscheinlichkeit; (Math.); Gesamtdarstellung",
}
@Article{Vanichpun:2004:OCU,
author = "Sarut Vanichpun and Armand M. Makowski",
title = "The output of a cache under the independent reference
model: where did the locality of reference go?",
journal = j-SIGMETRICS,
volume = "32",
number = "1",
pages = "295--306",
month = jun,
year = "2004",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1012888.1005722",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Fri Jun 27 09:21:18 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "We consider a cache operating under a demand-driven
replacement policy when document requests are modeled
according to the Independent Reference Model (IRM). We
characterize the popularity pmf of the stream of misses
from the cache, the so-called output of the cache, for
a large class of demand-driven cache replacement
policies. We measure strength of locality of reference
in a stream of requests through the skewness of its
popularity distribution. Using the notion of
majorization to capture this degree of skewness, we
show that for the policy $ A_0 $ and the random policy,
the output always has less locality of reference than
the input. However, we show by counterexamples that
this is not always the case under the LRU and CLIMB
policies when the input is selected according to a
Zipf-like pmf. In that case, conjectures are offered
(and supported by simulations) as to when LRU or CLIMB
caching indeed reduces locality of reference.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
journal-URL = "http://portal.acm.org/toc.cfm?id=J618",
keywords = "locality of reference; majorization; output of a
cache; popularity",
}
@Article{Anonymous:2005:UZL,
author = "Anonymous",
title = "The use of {Zipf}'s law in animal communication
analysis",
journal = j-ANIM-BEHAV,
volume = "69",
number = "1",
pages = "??--??",
day = "20",
month = jan,
year = "2005",
CODEN = "ANBEA8",
DOI = "http://dx.doi.org/10.1016/j.anbehav.2004.08.004",
ISSN = "0003-3472 (print), 1095-8282 (electronic)",
ISSN-L = "0003-3472",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0003347204003471",
acknowledgement = ack-nhfb,
fjournal = "Animal Behaviour",
journal-URL = "http://www.sciencedirect.com/science/journal/00033472",
keywords = "Zipf's Law",
}
@Article{Antonini:2005:RSC,
author = "Rita Giuliano Antonini and Georges Grekos",
title = "Regular sets and conditional density: an extension of
{Benford}'s law",
journal = j-COLLOQ-MATH,
volume = "103",
number = "2",
pages = "173--192",
year = "2005",
CODEN = "CQMAAQ",
DOI = "http://dx.doi.org/10.4064/cm103-2-3",
ISSN = "0010-1354 (print), 1730-6302 (electronic)",
ISSN-L = "0010-1354",
MRclass = "11B05 (11K99)",
MRnumber = "2197847 (2006j:11012)",
MRreviewer = "Radhakrishnan Nair",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "1092.11009",
acknowledgement = ack-nhfb,
fjournal = "Colloquium Mathematicum",
keywords = "asymptotic density; Benford's law; conditional
density; first digit problem; logarithmic density;
regular set; regular varying function",
ZMclass = "11B05 (Topology etc. of sets of numbers); 11K99
(Probabilistic theory)",
}
@Article{Berger:2005:BLP,
author = "Arno Berger",
title = "{Benford}'s law in power-like dynamical systems",
journal = j-STOCH-DYNAM,
volume = "5",
number = "4",
pages = "587--607",
year = "2005",
CODEN = "????",
DOI = "http://dx.doi.org/10.1142/S0219493705001602",
ISSN = "0219-4937",
ISSN-L = "0219-4937",
MRclass = "37B55 (11K06 37A50 37E05)",
MRnumber = "2185507 (2008i:37029)",
MRreviewer = "Peter Raith",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Stoch. Dyn.",
fjournal = "Stochastics and Dynamics",
}
@InCollection{Berger:2005:DDU,
author = "A. Berger",
booktitle = "{EQUADIFF} 2003",
title = "Dynamics and digits: on the ubiquity of {Benford}'s
law",
publisher = "World Sci. Publ., Hackensack, NJ",
pages = "693--695",
year = "2005",
DOI = "http://dx.doi.org/10.1142/9789812702067_0115",
MRclass = "37A45 (11K55)",
MRnumber = "2185113",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Berger:2005:MDD,
author = "Arno Berger",
title = "Multi-dimensional dynamical systems and {Benford}'s
law",
journal = j-DISCRETE-CONTIN-DYN-SYST,
volume = "13",
number = "1",
pages = "219--237",
year = "2005",
CODEN = "????",
DOI = "http://dx.doi.org/10.3934/dcds.2005.13.219",
ISSN = "1078-0947 (print), 1553-5231 (electronic)",
ISSN-L = "1078-0947",
MRclass = "37A45 (11K36 28D05 37A50 60F05)",
MRnumber = "2128801 (2005m:37016)",
MRreviewer = "Reinhard Winkler",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Continuous Dynamical Systems. Series A",
}
@Article{Berger:2005:ODD,
author = "Arno Berger and Leonid A. Bunimovich and Theodore P.
Hill",
title = "One-dimensional dynamical systems and {Benford}'s
law",
journal = j-TRANS-AM-MATH-SOC,
volume = "357",
number = "1",
pages = "197--219",
year = "2005",
CODEN = "TAMTAM",
DOI = "http://dx.doi.org/10.1090/S0002-9947-04-03455-5",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "37A45 (11K06 37A50 37E05 60F05 82B05)",
MRnumber = "2098092 (2005m:37017)",
MRreviewer = "Peter Raith",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
}
@Article{Bhattacharya:2005:CPA,
author = "Sukanto Bhattacharya and Kuldeep Kumar and Florentin
Smarandache",
title = "Conditional probability of actually detecting a
financial fraud --- a neutrosophic extension to
{Benford}'s law",
journal = "International Journal of Applied Mathematics",
volume = "17",
number = "1",
pages = "7--14",
year = "2005",
CODEN = "????",
ISSN = "1311-1728",
MRclass = "62G10 (91B28)",
MRnumber = "2170667",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/math/0504520",
abstract = "This study actually draws from and builds on an
earlier paper (Kumar and Bhattacharya, 2002). Here we
have basically added a neutrosophic dimension to the
problem of determining the conditional probability that
a financial fraud has been actually committed, given
that no Type I error occurred while rejecting the null
hypothesis H0: The observed first-digit frequencies
approximate a Benford distribution; and accepting the
alternative hypothesis H1: The observed first-digit
frequencies do not approximate a Benford distribution.
We have also suggested a conceptual model to implement
such a neutrosophic fraud detection system.",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Appl. Math.",
fjournal = "International Journal of Applied Mathematics",
}
@Article{Bhattacharyya:2005:COP,
author = "P. Bhattacharyya and A. Chatterjee and B. K.
Chakrabarti",
title = "A common origin of the power law distributions in
models of market and earthquake",
journal = "ArXiv e-prints",
year = "2005",
bibdate = "Sat Feb 16 17:25:18 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/physics/0510038",
acknowledgement = ack-nhfb,
}
@Article{Brown:2005:BLS,
author = "Richard J. C. Brown",
title = "{Benford}'s law and the screening of analytical data:
the case of pollutant concentrations in ambient air",
journal = j-ANALYST,
volume = "130",
number = "9",
pages = "1280--1285",
month = "????",
year = "2005",
CODEN = "ANALAO",
DOI = "http://dx.doi.org/10.1039/B504462F",
ISSN = "0003-2654 (print), 1364-5528 (electronic)",
ISSN-L = "0003-2654",
bibdate = "Sat Feb 16 17:27:51 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.ncbi.nlm.nih.gov/pubmed/16096674",
acknowledgement = ack-nhfb,
fjournal = "The Analyst",
}
@Article{Campi:2005:ZLM,
author = "X. Campi and H. Krivine",
title = "{Zipf}'s law in multifragmentation",
journal = j-PHYS-REV-C,
volume = "72",
number = "??",
pages = "057602",
day = "30",
month = nov,
year = "2005",
CODEN = "PRVCAN",
DOI = "http://dx.doi.org/10.1103/PhysRevC.72.057602",
ISSN = "0556-2813 (print), 1089-490X, 1538-4497",
ISSN-L = "0556-2813",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevC.72.057602",
acknowledgement = ack-nhfb,
fjournal = "Physical Review C (Nuclear Physics)",
journal-URL = "http://prc.aps.org/browse",
keywords = "Zipf's Law",
}
@TechReport{Ciofalo:2005:EBF,
author = "Michele Ciofalo",
title = "Entropy, {Benford}'s first digit law, and the
distribution of everything",
type = "Report",
institution = "Dipartimento di Ingegneria Nucleare, Universit{\`a}
degli Studi di Palermo",
address = "Palermo, Italy",
pages = "34",
year = "2005",
bibdate = "Sun Feb 17 08:23:55 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.din.unipa.it/Struttura/Personale/Profili/ciofalo_allegati/Paper_Benford.pdf",
acknowledgement = ack-nhfb,
}
@Article{Cleary:2005:ADA,
author = "Richard Cleary and Jay C. Thibodeau",
title = "Applying Digital Analysis Using {Benford's Law} to
Detect Fraud: The Dangers of Type {I} Errors",
journal = j-AUDITING,
volume = "24",
number = "1",
pages = "77--81",
month = may,
year = "2005",
CODEN = "????",
DOI = "http://dx.doi.org/10.2308/aud.2005.24.1.77",
ISSN = "0278-0380 (print), 1558-7991 (electronic)",
ISSN-L = "0278-0380",
bibdate = "Tue Nov 15 09:17:46 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://aaapubs.org/loi/ajpt;
http://link.aip.org/link/AJPTXX/v24/i1/p77/s1",
acknowledgement = ack-nhfb,
fjournal = "Auditing: A Journal of Practice \& Theory",
}
@Article{Cohen:2005:PCL,
author = "Edith Cohen and Carsten Lund",
title = "Packet classification in large {ISPs}: design and
evaluation of decision tree classifiers",
journal = j-SIGMETRICS,
volume = "33",
number = "1",
pages = "73--84",
month = jun,
year = "2005",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1064212.1064222",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Fri Jun 27 09:21:27 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "Packet classification, although extensively studied,
is an evolving problem. Growing and changing needs
necessitate the use of larger filters with more complex
rules. The increased complexity and size pose
implementation challenges on current hardware solutions
and drive the development of software classifiers, in
particular, decision-tree based classifiers. Important
performance measures for these classifiers are time and
memory due to required high throughput and use of
limited fast memory. We analyze Tier 1 ISP data that
includes filters and corresponding traffic from over a
hundred edge routers and thousands of interfaces. We
provide a comprehensive view on packet classification
in an operational network and glean insights that help
us design more effective classification algorithms. We
propose and evaluate decision tree classifiers with
{\em common branches}. These classifiers have linear
worst-case memory bounds and require much less memory
than standard decision tree classifiers, but
nonetheless, we show that on our data have similar
average and worst-case time performance. We argue that
common-branches exploit structure that is present in
real-life data sets. We observe a strong Zipf-like
pattern in the usage of rules in a classifier, where a
very small number of rules resolves the bulk of traffic
and most rules are essentially never used. Inspired by
this observation, we propose {\em traffic-aware\/}
classifiers that obtain superior average-case and
bounded worst-case performance. Good average-case can
boost performance of software classifiers that can be
used in small to medium sized routers and are also
important for traffic analysis and traffic
engineering.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
journal-URL = "http://portal.acm.org/toc.cfm?id=J618",
keywords = "access control lists; decision trees; packet
filtering; routing",
}
@Article{Dahui:2005:TRZ,
author = "Wang Dahui and Li Menghui and Di Zengru",
title = "True reason for {Zipf}'s law in language",
journal = j-PHYSICA-A,
volume = "358",
number = "2--4",
pages = "545--550",
day = "15",
month = dec,
year = "2005",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2005.04.021",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437105004085",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@InProceedings{DelAcebo:2005:BLN,
author = "Esteve {Del Acebo} and Mateu Sbert",
title = "{Benford's Law} for Natural and Synthetic Images",
crossref = "Neumann:2005:CAE",
pages = "169--176",
year = "2005",
DOI = "http://dx.doi.org/10.2312/COMPAESTH/COMPAESTH05/169-176",
bibdate = "Tue Nov 15 08:46:47 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.eg.org/EG/DL/WS/COMPAESTH/COMPAESTH05/169-176.pdf",
acknowledgement = ack-nhfb,
}
@Book{Durrett:2005:PTE,
author = "Richard Durrett",
title = "Probability: theory and examples",
publisher = "Thomson Brooks\slash Cole",
address = "Belmont, CA, USA",
edition = "Third",
pages = "xi + 497",
year = "2005",
ISBN = "0-534-42441-4",
ISBN-13 = "978-0-534-42441-1",
LCCN = "QA273 .D865 2005",
bibdate = "Mon Nov 21 10:00:11 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Duxbury advanced series",
acknowledgement = ack-nhfb,
remark = "Benford's Law is treated on pp. 337ff. Hill \cite[page
893]{Hill:1995:BII} reports that the 1991 edition has a
proof that the $k$-th digit of powers of integers
follows Benford's Law.",
subject = "Probabilities",
}
@Book{Egghe:2005:PLI,
author = "Leo Egghe",
title = "Power laws in the information production process:
{Lotkaian} informetrics",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "xvii + 427",
year = "2005",
ISBN = "0-12-088753-3, 0-08-048011-X (e-book)",
ISBN-13 = "978-0-12-088753-8, 978-0-08-048011-4 (e-book)",
LCCN = "Z669.8 .E44 2005",
bibdate = "Mon Feb 25 10:42:26 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See pages 204--205 for Benford's Law discussion.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
subject-dates = "Lotka, Alfred James, (1880--1949)",
tableofcontents = "Basic theory of Lotkaian informetrics \\
Three-dimensional Lotkaian informetrics \\
Lotkaian concentration theory \\
Lotkaian fractal complexity theory \\
Lotkaian informetrics of systems in which items can
have multiple sources \\
Further applications in Lotkaian informetrics \\
Lotkaian informetrics: an introduction",
}
@Article{elSehity:2005:PDA,
author = "Tarek el Sehity and Erik Hoelzl and Erich Kirchler",
title = "Price developments after a nominal shock: {Benford's
Law} and psychological pricing after the euro
introduction",
journal = j-INT-J-RES-MARK,
volume = "22",
number = "4",
pages = "471--480",
month = dec,
year = "2005",
CODEN = "IJRME6",
DOI = "http://dx.doi.org/10.1016/j.ijresmar.2005.09.002",
ISSN = "0167-8116 (print), 1873-8001 (electronic)",
ISSN-L = "0167-8116",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167811605000522",
abstract = "Retail managers use psychological pricing to make the
prices of goods appear to be just below a round number.
The euro introduction in 2002, with its various
exchange rates, distorted existing nominal price
patterns while at the same time retaining real prices.
We studied consumer prices before and after the
introduction of the euro by using Benford's Law as a
benchmark for price adjustments. Results indicate the
usefulness of this benchmark for detecting
irregularities in prices, and a clear trend towards
psychological pricing after the nominal shock of the
euro introduction. In addition, the tendency towards
psychological prices results in different inflation
rates in dependence of the price pattern.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Research in Marketing",
keywords = "Benford's Law; Digital analysis; Price endings; Retail
pricing",
}
@Article{Fairthorne:2005:PDE,
author = "Robert A. Fairthorne",
title = "Progress in Documentation: Empirical Hyperbolic
Distributions ({Bradford--Zipf--Mandelbrot}) for
Bibliometric Description and Prediction",
journal = j-J-DOC,
volume = "61",
number = "2",
pages = "171--193",
month = "????",
year = "2005",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/00220410510585179",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 06:27:27 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Reprint of \cite{Fairthorne:1969:PDE}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
remark = "According to \cite{Potter:1981:LLR}, this paper is the
first to link the distributions of Bradford, Zipf,
Mandelbrot, and Lotka.",
}
@Article{FerreriCancho:2005:CZL,
author = "Ramon {Ferrer i Cancho} and Oliver Riordan and
B{\'e}la Bollob{\'a}s",
title = "The consequences of {Zipf}'s law for syntax and
symbolic reference",
journal = j-PROC-R-SOC-LOND-SER-B-BIO-SCI,
volume = "272",
number = "1562",
pages = "561--565",
day = "7",
month = mar,
year = "2005",
CODEN = "PRLBA4",
DOI = "http://dx.doi.org/10.1098/rspb.2004.2957",
ISSN = "0962-8452 (print), 1471-2954 (electronic)",
ISSN-L = "0962-8452",
bibdate = "Tue Nov 15 11:27:26 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://rspb.royalsocietypublishing.org/content/272/1562/561.full",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society of London. Series B.
Biological sciences",
}
@TechReport{Giles:2005:BLN,
author = "David E. Giles",
title = "{Benford's Law} and Naturally Occurring Prices in
Certain {ebaY} Auctions",
type = "Econometrics Working Paper",
number = "EWP0505",
institution = "Department of Economics, University of Victoria",
address = "Victoria, BC, Canada",
month = may,
year = "2005",
ISSN = "1485-6441",
bibdate = "Thu Feb 15 16:24:39 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://web.uvic.ca/econ/ewp0505.pdf",
abstract = "We show that certain the winning bids for certain ebaY
auctions obey Benford's Law. One implication of this is
that it is unlikely that these bids are subject to
collusion among bidders, or ``shilling'' on the part of
sellers. Parenthetically, we also show that numbers
from the naturally occurring Fibonacci and Lucas
sequences also obey Benford's Law.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Harremoes:2005:ZLHa,
author = "Peter Harremo{\"e}s and Flemming Topsoe",
title = "{Zipf}'s law, hyperbolic distributions and entropy
loss",
journal = j-PHYSICA-A,
volume = "328",
number = "3--4",
pages = "315--318",
day = "1",
month = aug,
year = "2005",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.endm.2005.07.075",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1571065305051450",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@InCollection{Harremoes:2005:ZLHb,
author = "Peter Harremo{\"e}s and Flemming Topsoe",
editor = "Rudolf Ahlswede and others",
booktitle = "General theory of information transfer and
combinatorics.",
title = "{Zipf}'s law, hyperbolic distributions and entropy
loss",
volume = "21",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "315--318",
year = "2005",
DOI = "http://dx.doi.org/10.1016/j.endm.2005.07.075",
bibdate = "Sat Nov 12 11:07:14 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Electronic Notes in Discrete Mathematics",
ZMnumber = "1158.91482",
abstract = "Zipf's law --- or Estoup-Zipf's law --- is an
empirical fact of computational linguistics which
relates rank and frequency of words in natural
languages. The law suggests modelling by distributions
of ``hyperbolic type''. We present a satisfactory
general definition and an information-theoretical
characterization of the resulting hyperbolic
distributions. When applied to linguistics this leads
to a property of stability and flexibility, explaining
that a language can develop towards higher and higher
expressive powers without changing its basic
structure.",
acknowledgement = ack-nhfb,
classmath = "91F20 (Linguistics) 94A15 (General topics of
information theory) 94A17 (Measures of information)",
keywords = "entropy loss; hyperbolic distributions; Zipf's law",
}
@Article{Hill:2005:RDS,
author = "Theodore P. Hill and Klaus Sch{\"u}rger",
title = "Regularity of digits and significant digits of random
variables",
journal = j-STOCH-PROC-APPL,
volume = "115",
number = "10",
pages = "1723--1743",
month = oct,
year = "2005",
CODEN = "STOPB7",
DOI = "http://dx.doi.org/10.1016/j.spa.2005.05.003",
ISSN = "0304-4149 (print), 1879-209X (electronic)",
ISSN-L = "0304-4149",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0304414905000657",
abstract = "A random variable X is digit-regular (respectively,
significant-digit-regular) if the probability that
every block of k given consecutive digits (significant
digits) appears in the b-adic expansion of X approaches
b - k as the block moves to the right, for all integers
b > 1 and k 1 . Necessary and sufficient conditions are
established, in terms of convergence of Fourier
coefficients, and in terms of convergence in
distribution modulo 1, for a random variable to be
digit-regular (significant-digit-regular), and basic
relationships between digit-regularity and various
classical classes of probability measures and normal
numbers are given. These results provide a theoretical
basis for analyses of roundoff errors in numerical
algorithms which use floating-point arithmetic, and for
detection of fraud in numerical data via using
goodness-of-fit of the least significant digits to
uniform, complementing recent tests for leading
significant digits based on Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "Stochastic Processes and Their Applications",
keywords = "Benford's Law; Digit-regular random variable;
Floating-point numbers; Law of least significant
digits; Nonleading digits; Normal numbers; Significant
digits; Significant-digit-regular random variable;
Trailing digits",
}
@InProceedings{Hjorland:2005:BLS,
author = "Birger Hj{\o}rland and Jeppe Nicolaisen",
editor = "Fabio Crestani and Ian Ruthven",
booktitle = "Context: nature, impact, and role: {5th International
Conference on Conceptions of Library and Information
Sciences, CoLIS 2005, Glasgow, UK, June 4--8, 2005;
proceedings}",
title = "{Bradford}'s law of scattering: ambiguities in the
concept of ``subject''",
volume = "3507",
publisher = pub-SV,
address = pub-SV:adr,
pages = "96--106",
year = "2005",
ISBN = "3-540-26178-8",
ISBN-13 = "978-3-540-26178-0",
LCCN = "Z672.5 .I5616 2005",
bibdate = "Fri Nov 25 11:52:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
bookpages = "xiii + 250",
}
@Article{Ioannidis:2005:WMP,
author = "John P. A. Ioannidis",
title = "Why Most Published Research Findings Are False",
journal = j-PLOS-MED,
volume = "2",
number = "8",
pages = "696--701",
month = aug,
year = "2005",
CODEN = "PMLEAC",
DOI = "http://dx.doi.org/10.1371/journal.pmed.0020124",
ISSN = "1549-1277 (print), 1549-1676 (electronic)",
ISSN-L = "1549-1277",
bibdate = "Fri Nov 18 12:42:05 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020124",
abstract = "There is increasing concern that most current
published research findings are false. The probability
that a research claim is true may depend on study power
and bias, the number of other studies on the same
question, and, importantly, the ratio of true to no
relationships among the relationships probed in each
scientific field. In this framework, a research finding
is less likely to be true when the studies conducted in
a field are smaller; when effect sizes are smaller;
when there is a greater number and lesser preselection
of tested relationships; where there is greater
flexibility in designs, definitions, outcomes, and
analytical modes; when there is greater financial and
other interest and prejudice; and when more teams are
involved in a scientific field in chase of statistical
significance. Simulations show that for most study
designs and settings, it is more likely for a research
claim to be false than true. Moreover, for many current
scientific fields, claimed research findings may often
be simply accurate measures of the prevailing bias. In
this essay, I discuss the implications of these
problems for the conduct and interpretation of
research.",
acknowledgement = ack-nhfb,
articleno = "e124",
fjournal = "PLoS Medicine",
journal-URL = "http://medicine.plosjournals.org/",
remark = "This article does not discuss Benford's Law, but is
related to the use of that law in the detection of
fraud in research data. Ioannidis discusses the abuse
of statistics for limited experimental data, a topic
that receives book-length treatment in
\cite{Ziliak:2008:CSS}.",
}
@Article{Jolissaint:2005:LBR,
author = "Paul Jolissaint",
title = "Loi de {Benford}, relations de r{\'e}currence et
suites {\'e}quidistribu{\'e}es. ({French}) [{Benford}'s
Law, recurrence relations, and equidistributed
sequences]",
journal = j-ELEM-MATH,
volume = "60",
number = "1",
pages = "10--18",
year = "2005",
CODEN = "????",
DOI = "http://dx.doi.org/10.4171/EM/2",
ISSN = "0013-6018 (print), 1420-8962 (electronic)",
ISSN-L = "0013-6018",
MRclass = "11K36 (37A45 60E99)",
MRnumber = "2188341 (2006j:11109)",
MRreviewer = "Radhakrishnan Nair",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Elemente der Mathematik",
language = "French",
}
@Article{Kechedzhi:2005:RDW,
author = "K. E. Kechedzhi and O. V. Usatenko and V. A.
Yampol{\cprime}skii",
title = "Rank distributions of words in correlated symbolic
systems and the {Zipf} law",
journal = j-PHYS-REV-E,
volume = "72",
number = "4",
pages = "046138",
day = "28",
month = oct,
year = "2005",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.72.046138",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
MRclass = "82C31",
MRnumber = "2183723 (2006f:82069)",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.72.046138",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
pagecount = "6",
}
@Article{Kontorovich:2005:BLV,
author = "Alex V. Kontorovich and Steven J. Miller",
title = "{Benford}'s law, values of {$L$}-functions and the {$
3 x + 1 $} problem",
journal = j-ACTA-ARITHMETICA,
volume = "120",
number = "3",
pages = "269--297",
year = "2005",
CODEN = "AARIA9",
DOI = "http://dx.doi.org/10.4064/aa120-3-4",
ISSN = "0065-1036 (print), 1730-6264 (electronic)",
ISSN-L = "0065-1036",
MRclass = "11K06 (11B37 11M06 37A45)",
MRnumber = "2188844 (2007c:11085)",
MRreviewer = "J. C. Lagarias",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2005AcAri.120..269K;
http://arxiv.org/abs/math/0412003",
abstract = "We show the leading digits of a variety of systems
satisfying certain conditions follow Benford's Law. For
each system proving this involves two main ingredients.
One is a structure theorem of the limiting
distribution, specific to the system. The other is a
general technique of applying Poisson Summation to the
limiting distribution. We show the distribution of
values of $L$-functions near the central line and (in
some sense) the iterates of the $ 3 x + 1 $ Problem are
Benford.",
acknowledgement = ack-nhfb,
fjournal = "Acta Arithmetica",
}
@Article{Kulikova:2005:CAS,
author = "A. A. Kulikova and Yu. V. Prokhorov",
title = "Completely Asymmetric Stable Laws and {Benford's
Law}",
journal = j-THEORY-PROBAB-APPL,
volume = "49",
number = "1",
pages = "163--169",
month = mar,
year = "2005",
CODEN = "TPRBAU",
DOI = "http://dx.doi.org/10.1137/S0040585X97980944",
ISSN = "0040-585X (print), 1095-7219 (electronic)",
ISSN-L = "0040-585X",
bibdate = "Thu Jul 7 19:15:48 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/49/1;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/98094",
acknowledgement = ack-nhfb,
fjournal = "Theory of probability and its applications",
journal-URL = "http://epubs.siam.org/tvp",
keywords = "Benford's Law; Zipf's Law",
}
@Article{Kulikova:2005:HFD,
author = "A. A. Kulikova and Yu. V. Prokhorov and V. I.
Khokhlov",
title = "{H. F. D.} ({$H$}-function distribution) and the
{Benford} law. {I}",
journal = "Teor. Veroyatn. Primen.",
volume = "50",
number = "2",
pages = "366--371",
year = "2005",
CODEN = "????",
DOI = "http://dx.doi.org/10.1137/S0040585X97981706",
ISSN = "0040-361X",
ISSN-L = "0040-361X",
MRclass = "60E07 (60F05)",
MRnumber = "2221718 (2007b:60029)",
MRreviewer = "S{\'a}ndor Cs{\"o}rg{\H{o}}",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoriya
Veroyatnoste{\u\i} i ee Primeneniya",
}
@Article{Lagarias:2005:BLF,
author = "J. C. Lagarias and K. Soundararajan",
title = "{Benford}'s law for the $ 3 x + 1 $ function",
journal = "ArXiv Mathematics e-prints",
month = sep,
year = "2005",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2005math......9175L;
http://arxiv.org/abs/math/0509175",
acknowledgement = ack-nhfb,
eprint = "arXiv:math/0509175",
keywords = "Mathematics - Number Theory, Mathematics -
Probability",
}
@Article{Li:2005:ZLP,
author = "Yujian Li and Chuangbai Xiao",
title = "{Zipf}'s law probably existing in protein sequences",
journal = "J. Beijing Univ. Technol.",
volume = "31",
number = "4",
pages = "366--368",
year = "2005",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Nov 12 11:10:06 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "1084.92019",
abstract = "In order to analyze whether Zipf's law in linguistics
exists in protein sequences, this paper uses $ 1.735 \,
7 \times 10^4 $ protein sequences labeled with
secondary structures which are selected from the DSSP
database. The segments of successive amino acid
residues with a same code of secondary structure are
defined as words. The results show that the
distribution of words emerging frequency follows Zipf's
law with the exponent $ 0.981 $.",
acknowledgement = ack-nhfb,
classmath = "92C40 (Biochemistry, etc.); 62P10 (Appl. of statistics
to biology): 92D20 (Protein sequences, DNA sequences)",
language = "Chinese. English summary",
xxremark = "Which journal is this? Beijing gong ye da xue xue bao
= Journal of Beijing Polytechnic University (ISSN
0254-0037), or Beijing ke ji da xue xue bao = Journal
of University of Science and Technology, Beijing (ISSN
1001-053X), or something different?",
}
@Article{Lu:2005:CZL,
author = "Tim Lu and Christine M. Costello and Peter J. P.
Croucher and Robert H{\"a}sler and G{\"u}nther Deuschl
and Stefan Schreiber",
title = "Can {Zipf}'s law be adapted to normalize
microarrays?",
journal = j-BMC-BIOINFORMATICS,
volume = "6",
number = "??",
pages = "37--49",
month = "????",
year = "2005",
CODEN = "BBMIC4",
DOI = "http://dx.doi.org/10.1186/1471-2105-6-37",
ISSN = "1471-2105",
ISSN-L = "1471-2105",
bibdate = "Sat Feb 16 18:38:50 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.biomedcentral.com/1471-2105/6/37",
acknowledgement = ack-nhfb,
fjournal = "BMC Bioinformatics",
journal-URL = "http://www.biomedcentral.com/bmcbioinformatics/",
}
@InProceedings{Lu:2005:DFH,
author = "Fletcher Lu and J. Efrim Boritz",
title = "Detecting Fraud in Health Insurance Data: Learning to
Model Incomplete {Benford's Law} Distributions",
crossref = "Gama:2005:MLE",
pages = "633--640",
year = "2005",
DOI = "http://dx.doi.org/10.1007/11564096_63",
bibdate = "Tue Nov 15 08:55:45 2011",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/ecml/ecml2005.html#LuB05;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@Article{Ma:2005:CBL,
author = "Y. G. Ma and J. B. Natowitz and R. Wada and K. Hagel
and J. Wang and T. Keutgen and Z. Majka and M. Murray
and L. Qin and P. Smith and R. Alfaro and J. Cibor and
M. Cinausero and Y. El Masri and D. Fabris and E.
Fioretto and A. Keksis and M. Lunardon and A. Makeev
and N. Marie and E. Martin and A. Martinez-Davalos and
A. Menchaca-Rocha and G. Nebbia and G. Prete and V.
Rizzi and A. Ruangma and D. V. Shetty and G. Souliotis
and P. Staszel and M. Veselsky and G. Viesti and E. M.
Winchester and S. J. Yennello",
title = "Critical behavior in light nuclear systems:
Experimental aspects",
journal = j-PHYS-REV-C,
volume = "71",
number = "5",
pages = "054606",
day = "26",
month = may,
year = "2005",
CODEN = "PRVCAN",
DOI = "http://dx.doi.org/10.1103/PhysRevC.71.054606",
ISSN = "0556-2813 (print), 1089-490X, 1538-4497",
ISSN-L = "0556-2813",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevC.71.054606",
acknowledgement = ack-nhfb,
fjournal = "Physical Review C (Nuclear Physics)",
journal-URL = "http://prc.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Manaris:2005:ZLM,
author = "Bill Manaris and Juan Romero and Penousal Machado and
Dwight Krehbiel and Timothy Hirzel and Walter Pharr and
Robert B. Davis",
title = "{Zipf}'s law, music classification, and aesthetics",
journal = j-COMP-MUSIC-J,
volume = "29",
number = "1",
pages = "55--69",
month = "Spring",
year = "2005",
CODEN = "CMUJDY",
ISSN = "0148-9267 (print), 1531-5169 (electronic)",
ISSN-L = "0148-9267",
bibdate = "Sat Feb 16 18:40:14 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://muse.jhu.edu/journals/cmj/summary/v029/29.1manaris.html;
http://muse.jhu.edu/journals/computer_music_journal/v029/29.1manaris.pdf",
acknowledgement = ack-nhfb,
fjournal = "Computer Music Journal",
keywords = "Benford's Law; Zipf's Law; Zipf--Mandelbrot Law",
}
@Article{Maslov:2005:GTS,
author = "V. P. Maslov",
title = "On a general theorem of set theory that leads to the
{Gibbs}, {Bose--Einstein}, and {Pareto} distributions
and to the {Zipf--Mandelbrot} law for the stock
market",
journal = j-MAT-ZAMETKI,
volume = "78",
number = "6",
pages = "870--877",
year = "2005",
CODEN = "????",
DOI = "http://dx.doi.org/10.1007/s11006-005-0186-9",
ISSN = "0025-567X",
ISSN-L = "0025-567X",
MRclass = "91B28 (90C29)",
MRnumber = "2249037 (2007b:91077)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
Zametki",
}
@Article{Maslov:2005:RZLa,
author = "V. P. Maslov",
title = "Refining {Zipf}'s law for frequency dictionaries",
journal = j-DOKL-AKAD-NAUK,
volume = "405",
number = "5",
pages = "591--594",
year = "2005",
CODEN = "DANKAS",
ISSN = "0869-5652",
ISSN-L = "0869-5652",
MRclass = "94A15 (60C05)",
MRnumber = "2340762",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii
Nauk",
}
@Article{Maslov:2005:RZLb,
author = "V. P. Maslov",
title = "Refinement of {Zipf}'s law for frequency
dictionaries",
journal = j-DOKL-MATH,
volume = "72",
number = "3",
pages = "942--945",
year = "2005",
CODEN = "????",
ISSN = "1064-5624 (print), 1531-8362 (electronic)",
ISSN-L = "1064-5624",
bibdate = "Sat Nov 12 11:05:14 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "1206.82009",
acknowledgement = ack-nhfb,
classmath = "82B10 (Quantum equilibrium statistical mechanics
(general)) 68T50 (Natural language processing) 68Q45
(Formal languages)",
fjournal = "Doklady Mathematics",
keywords = "Bose--Einstein statistics",
language = "English. Russian original",
}
@Article{Maslov:2005:ZML,
author = "V. P. Maslov",
title = "The {Zipf--Mandelbrot} law: quantization and an
application to the stock market",
journal = j-RUSS-J-MATH-PHYS,
volume = "12",
number = "4",
pages = "483--488",
year = "2005",
CODEN = "RJMPEL",
ISSN = "1061-9208",
ISSN-L = "1061-9208",
MRclass = "91B28 (82B99)",
MRnumber = "2201312 (2006i:91053)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Russian Journal of Mathematical Physics",
}
@Article{McAllister:2005:ACE,
author = "James W. McAllister",
title = "Algorithmic compression of empirical data: reply to
{Twardy}, {Gardner}, and {Dowe}",
journal = j-STUD-HIST-PHILOS-SCI,
volume = "36",
number = "2",
pages = "403--410",
month = jun,
year = "2005",
CODEN = "SHPSB5",
DOI = "http://dx.doi.org/10.1016/j.shpsa.2005.04.005",
ISSN = "0039-3681 (print), 1879-2510 (electronic)",
ISSN-L = "0039-3681",
bibdate = "Mon Nov 7 12:11:58 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/shps-a.bib;
http://www.sciencedirect.com/science/journal/00393681",
note = "See \cite{McAllister:2003:ARE,Twardy:2005:EDS}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0039368105000221",
acknowledgement = ack-nhfb,
fjournal = "Studies in History and Philosophy of Science Part A",
journal-URL = "http://www.sciencedirect.com/science/journal/00393681",
}
@Article{McCowan:2005:AUZ,
author = "B. McCowan and L. R. Doyle and J. M. Jenkins and S. F.
Hanser",
title = "The appropriate use of {Zipf}'s law in animal
communication studies",
journal = j-ANIM-BEHAV,
volume = "69",
number = "1",
pages = "F1--F7",
day = "20",
month = jan,
year = "2005",
CODEN = "ANBEA8",
DOI = "http://dx.doi.org/10.1016/j.anbehav.2004.09.002",
ISSN = "0003-3472 (print), 1095-8282 (electronic)",
ISSN-L = "0003-3472",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S000334720400346X",
acknowledgement = ack-nhfb,
fjournal = "Animal Behaviour",
journal-URL = "http://www.sciencedirect.com/science/journal/00033472",
keywords = "Zipf's Law",
}
@Article{Miller:2005:BLV,
author = "S. J. Miller and A. Kontorovich",
title = "{Benford}'s law, values of {$L$}-functions and the $ 3
x + 1 $ problem",
journal = j-ACTA-ARITHMETICA,
volume = "120",
number = "3",
pages = "269--297",
month = "????",
year = "2005",
CODEN = "AARIA9",
DOI = "http://dx.doi.org/10.4064/aa120-3-4",
ISSN = "0065-1036 (print), 1730-6264 (electronic)",
ISSN-L = "0065-1036",
MRclass = "11K06, 60A10, 11B83, 11M06 (60F05, 11J86, 60J65,
46F12)",
bibdate = "Tue Feb 26 06:11:26 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Acta Arithmetica",
}
@InProceedings{Nagasaka:2005:BLD,
author = "Kenji Nagasaka",
editor = "G. Barat and H. Daud{\'e} and M. Laurent and P.
Liardet and S. Louboutin and A. Thomas",
booktitle = "{Journ{\'e}es Arithm{\'e}tiques XXIV, Marseilles, July
4--8, 2005, Universit{\'e} de Provence and
Universit{\'e} de la M{\'e}diterran{\'e}e and CNRS
Marseilles, France}",
title = "{Benford}'s law with different basis",
publisher = "????",
address = "????",
pages = "1--2",
year = "2005",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 18:49:26 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://atlas-conferences.com/c/a/r/e/47.htm",
acknowledgement = ack-nhfb,
}
@Article{Newman:2005:PLP,
author = "M. E. J. Newman",
title = "Power laws, {Pareto} distributions and {Zipf}'s law",
journal = j-CONTEMP-PHYS,
volume = "46",
number = "5",
pages = "323--351",
month = sep,
year = "2005",
CODEN = "CTPHAF",
DOI = "http://dx.doi.org/10.1080/00107510500052444",
ISSN = "0010-7514 (print), 1366-5812 (electronic)",
ISSN-L = "0010-7514",
bibdate = "Fri Jul 09 16:33:18 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "When the probability of measuring a particular value
of some quantity varies inversely as a power of that
value, the quantity is said to follow a power law, also
known variously as Zipf's law or the Pareto
distribution. Power laws appear widely in physics,
biology, earth and planetary sciences, economics and
finance, computer science, demography and the social
sciences. For instance, the distributions of the sizes
of cities, earthquakes, forest fires, solar flares,
moon craters and people's personal fortunes all appear
to follow power laws. The origin of power-law behaviour
has been a topic of debate in the scientific community
for more than a century. Here we review some of the
empirical evidence for the existence of power-law forms
and the theories proposed to explain them.",
acknowledgement = ack-nhfb,
fjournal = "Contemporary physics",
keywords = "Benford's Law; critical phenomena; Legendre beta
function; Pareto distribution; percolation; phase
transitions; power-law distributions; random walks;
Riemann zeta function; scale-free distributions; Yule
process; Zipf's Law",
remark = "This article is an excellent survey of continuous and
discrete distributions that follow a power law, and
some that do not. It is well worth reading.",
subject = "astrophysics; atomic and nuclear physics; chemical
physics; computational physics; condensed matter
physics; environmental physics; experimental physics;
general physics; particle and high energy physics;
plasma physics; space science; theoretical physics",
}
@Article{Nigrini:2005:ACI,
author = "Mark Nigrini",
title = "An assessment of the change in the incidence of
earnings management around the {Enron--Andersen}
episode",
journal = "Review of Accounting and Finance",
volume = "4",
number = "1",
pages = "92--110",
month = "????",
year = "2005",
DOI = "http://dx.doi.org/10.1108/eb043420",
ISSN = "1475-7702 (print), 1758-7700 (electronic)",
ISSN-L = "1475-7702",
bibdate = "Fri Mar 22 09:08:37 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.emeraldinsight.com/journals.htm?issn=1475-7702&volume=4&issue=1&articleid=1657234",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
}
@Article{Nitsch:2005:ZZ,
author = "Volker Nitsch",
title = "{Zipf} zipped",
journal = j-J-URBAN-ECON,
volume = "57",
number = "1",
pages = "86--100",
day = "15",
month = jan,
year = "2005",
CODEN = "JUECDW",
DOI = "http://dx.doi.org/10.1016/j.jue.2004.09.002",
ISSN = "0094-1190 (print), 1095-9068 (electronic)",
ISSN-L = "0094-1190",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0094119004000981",
acknowledgement = ack-nhfb,
fjournal = "Journal of Urban Economics",
journal-URL = "http://www.sciencedirect.com/science/journal/00941190",
keywords = "Zipf's Law",
}
@Article{Perline:2005:SWF,
author = "Richard Perline",
title = "Strong, weak and false inverse power laws",
journal = j-STAT-SCI,
volume = "20",
number = "1",
pages = "68--88",
month = "????",
year = "2005",
CODEN = "STSCEP",
ISSN = "0883-4237",
ISSN-L = "0883-4237",
bibdate = "Fri Nov 18 12:15:56 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Statistical Science",
journal-URL = "http://projecteuclid.org/all/euclid.ss",
keywords = "Benford's Law",
}
@Book{Posch:2005:ZTP,
author = "Peter N. Posch",
title = "{Ziffernanalyse in Theorie und Praxis: Testverfahren
zur F{\"a}lschungsaufsp{\"u}rung mit Benfords Gesetz}",
publisher = "Shaker",
address = "Aachen, Germany",
pages = "iv + 87 + v",
year = "2005",
ISBN = "3-8322-4492-1",
ISBN-13 = "978-3-8322-4492-7",
LCCN = "????",
bibdate = "Mon Feb 18 18:01:33 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.gbv.de:20011/gvk",
price = "EUR 29.80 (DE)",
series = "Berichte aus der Statistik",
URL = "http://www.gbv.de/dms/hbz/toc/ht014717371.pdf",
acknowledgement = ack-nhfb,
}
@Article{Rousseau:2005:RFE,
author = "Ronald Rousseau",
title = "{Robert Fairthorne} and the empirical power laws",
journal = j-J-DOC,
volume = "61",
number = "2",
pages = "194--202",
month = "????",
year = "2005",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/00220410510585188",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 06:42:00 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
remark = "Review of
\cite{Fairthorne:1969:PDE,Fairthorne:2005:PDE}.",
}
@Article{Rowlands:2005:EAD,
author = "Ian Rowlands",
title = "{Emerald} authorship data, {Lotka}'s law and research
productivity",
journal = j-ASLIB-PROC,
volume = "57",
number = "1",
pages = "5--10",
month = "????",
year = "2005",
CODEN = "ASLPAO",
DOI = "http://dx.doi.org/10.1108/00012530510579039",
ISSN = "0001-253X (print), 1758-3748 (electronic)",
ISSN-L = "0001-253X",
bibdate = "Fri Nov 25 07:25:01 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "ASLIB Proceedings",
keywords = "brand loyalty; publishing; research results",
remark = "This paper applies Lotka's Law to the question of the
likelihood of an author remaining with a particular
publisher.",
}
@Article{Shan:2005:GZD,
author = "Shi Shan",
title = "On the generalized {Zipf} distribution. {Part I}",
journal = j-INFO-PROC-MAN,
volume = "41",
number = "6",
pages = "1369--1386",
day = "1",
month = dec,
year = "2005",
CODEN = "IPMADK",
DOI = "http://dx.doi.org/10.1016/j.ipm.2005.03.003",
ISSN = "0306-4573 (print), 1873-5371 (electronic)",
ISSN-L = "0306-4573",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S030645730500018X",
acknowledgement = ack-nhfb,
fjournal = "Information Processing and Management",
keywords = "Zipf's Law",
}
@Article{Soo:2005:ZLC,
author = "Kwok Tong Soo",
title = "{Zipf's Law} for cities: a cross-country
investigation",
journal = j-REG-SCI-URBAN-ECON,
volume = "35",
number = "3",
pages = "239--263",
day = "1",
month = may,
year = "2005",
CODEN = "RSUEDM",
DOI = "http://dx.doi.org/10.1016/j.regsciurbeco.2004.04.004",
ISSN = "0166-0462 (print), 1879-2308 (electronic)",
ISSN-L = "0166-0462",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S016604620400033X",
acknowledgement = ack-nhfb,
fjournal = "Regional Science and Urban Economics",
journal-URL = "http://www.sciencedirect.com/science/journal/01660462",
keywords = "Zipf's Law",
}
@Article{Stadje:2005:APD,
author = "Wolfgang Stadje",
title = "Asymptotic properties of digit sequences of random
numbers",
journal = j-MATH-NACHR,
volume = "278",
number = "10",
pages = "1209--1229",
month = "????",
year = "2005",
CODEN = "MTMNAQ",
DOI = "http://dx.doi.org/10.1002/mana.200310303",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
bibdate = "Mon Feb 18 06:36:36 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "1073.11053",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
keywords = "ergodicity; limit theorem; Markov chain; moments;
occurrence probability; random digit sequence;
stationary digits; transition function",
ZMclass = "11K31 (Special sequences); 60G10 (Stationary
processes); 60J05 (Discrete-time Markov processes on
general state spaces); 60F99 (Limit theorems
(probability))",
}
@TechReport{Taylor:2005:TMT,
author = "Jonathan Taylor",
title = "Too many ties? An empirical analysis of the
{Venezuelan} recall referendum counts",
type = "Technical report",
number = "??",
institution = "Department of Statistics, Stanford University",
address = "Stanford, CA 94305, USA",
year = "2005",
bibdate = "Fri Feb 15 18:29:53 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://esdata.info/pdf/Taylor-Ties.pdf;
http://www.benfordonline.net/fullreference/577",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Pericchi:2011:QAD}, with ``Statist.
Sci. To appear 2009''. However, the article is not yet
found there in February 2013. This report was issued as
a result of the Carter Center's investigation of
fairness of 2004 voting in Venezuela. Its conclusion,
that there was no demonstrable electoral fraud, has
been challenged; see \cite{Pericchi:2011:QAD}.",
}
@Article{Twardy:2005:EDS,
author = "Charles Twardy and Steve Gardner and David L. Dowe",
title = "Empirical data sets are algorithmically compressible:
reply to {McAllister}?",
journal = j-STUD-HIST-PHILOS-SCI,
volume = "36",
number = "2",
pages = "391--402",
month = jun,
year = "2005",
CODEN = "SHPSB5",
DOI = "http://dx.doi.org/10.1016/j.shpsa.2005.04.004",
ISSN = "0039-3681 (print), 1879-2510 (electronic)",
ISSN-L = "0039-3681",
bibdate = "Mon Nov 7 12:11:58 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/shps-a.bib;
http://www.sciencedirect.com/science/journal/00393681",
note = "See \cite{McAllister:2003:ARE,McAllister:2005:ACE}.",
URL = "http://www.sciencedirect.com/science/article/pii/S003936810500021X",
acknowledgement = ack-nhfb,
fjournal = "Studies in History and Philosophy of Science Part A",
journal-URL = "http://www.sciencedirect.com/science/journal/00393681",
}
@Article{vanLeijenhorst:2005:FDH,
author = "D. C. van Leijenhorst and Th. P. van der Weide",
title = "A formal derivation of {Heaps}' law",
journal = j-INFO-SCI,
volume = "170",
number = "2--4",
pages = "263--272",
year = "2005",
CODEN = "ISIJBC",
DOI = "http://dx.doi.org/10.1016/j.ins.2004.03.006",
ISSN = "0020-0255 (print), 1872-6291 (electronic)",
ISSN-L = "0020-0255",
MRclass = "60C05",
MRnumber = "2120894 (2005h:60024)",
bibdate = "Sat Nov 12 10:28:06 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Word frequencies in text documents can be reasonably
described by the Mandelbrot distribution, which has
Zipf's law as a special case. Furthermore, the growth
of vocabulary size as a function of the text size (its
number of words) has been described in Heaps' law. It
has been shown that these two experimental laws are
related. In this paper we go a step further, and
provide a (formal) derivation of Heaps' law from the
Mandelbrot distribution. We also provide a
specification of the validity area for applying Heaps'
law.",
acknowledgement = ack-nhfb,
ajournal = "Inform. Sci.",
fjournal = "Information Sciences. An International Journal",
}
@Article{Aban:2006:PET,
author = "Inmaculada B. Aban and Mark M. Meerschaert and Anna K.
Panorska",
title = "Parameter Estimation for the Truncated {Pareto}
Distribution",
journal = j-J-AM-STAT-ASSOC,
volume = "101",
number = "473",
pages = "270--277",
month = mar,
year = "2006",
CODEN = "JSTNAL",
DOI = "http://dx.doi.org/10.1198/016214505000000411",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Thu Aug 26 11:26:31 MDT 2010",
bibsource = "http://www.amstat.org/publications/jasa/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc2000.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Baskerville:2006:SEM,
author = "Kim Baskerville and Maya Paczuski",
title = "Subgraph ensembles and motif discovery using an
alternative heuristic for graph isomorphism",
journal = j-PHYS-REV-E,
volume = "74",
number = "??",
pages = "051903",
day = "3",
month = nov,
year = "2006",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.74.051903",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.74.051903",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Bohachevsky:2006:DBL,
author = "Ihor O. Bohachevsky and Mark E. Johnson and Myron L.
Stein",
title = "A derivation of {Benford}'s law",
journal = j-AM-J-MATH-MANAGE-SCI,
volume = "26",
number = "3--4",
pages = "355--370",
year = "2006",
CODEN = "AMMSDX",
ISSN = "0196-6324",
ISSN-L = "0196-6324",
MRclass = "60E99 (11K36)",
MRnumber = "2312400 (2008h:60062)",
MRreviewer = "Radhakrishnan Nair",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Mathematical and Management
Sciences",
}
@InProceedings{Dallacasa:2006:TBS,
author = "F. Dallacasa and Valerio Dallacasa",
editor = "????",
booktitle = "{5th International Conference: APLIMAT 2006, Slovak
University of Technology, Bratislava}",
title = "Temporal behaviour of stock data from {Benford}'s
law",
publisher = "????",
address = "????",
pages = "425--432",
year = "2006",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 17:32:15 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
price = "US\$",
URL = "http://archiv.aplimat.com/2006/Aplimat/Proceedings/Communications/Financial_Actuary_math/Dallasca-Dallasca.pdf",
acknowledgement = ack-nhfb,
}
@Article{Dorogovtsev:2006:FON,
author = "S. N. Dorogovtsev and J. F. F. Mendes and J. G.
Oliveira",
title = "Frequency of occurrence of numbers in the {World Wide
Web}",
journal = j-PHYSICA-A,
volume = "360",
number = "2",
pages = "548--556",
month = feb,
year = "2006",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2005.06.064",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://arxiv.org/abs/physics/0504185;
http://www.sciencedirect.com/science/article/pii/S0378437105006874",
abstract = "The distribution of numbers in human documents is
determined by a variety of diverse natural and human
factors, whose relative significance can be evaluated
by studying the numbers frequency of occurrence.
Although it has been studied since the 1880's, this
subject remains poorly understood. Here, we obtain the
detailed statistics of numbers in the World Wide Web,
finding that their distribution is a heavy-tailed
dependence which splits in a set of power-law ones. In
particular, we find that the frequency of numbers
associated to western calendar years shows an uneven
behavior: 2004 represents a singular critical point,
appearing with a strikingly high frequency; as we move
away from it, the decreasing frequency allows us to
compare the amounts of existing information on the past
and on the future. Moreover, while powers of ten occur
extremely often, allowing us to obtain statistics up to
the huge 10 127, non-round numbers occur in a much more
limited range, the variations of their frequencies
being dramatically different from standard statistical
fluctuations. These findings provide a view of the
array of numbers used by humans as a highly
non-equilibrium and inhomogeneous system, and shed a
new light on an issue that, once fully investigated,
could lead to a better understanding of many
sociological and psychological phenomena.",
acknowledgement = ack-nhfb,
fjournal = "Physica A: Statistical Mechanics and its
Applications",
keywords = "Benford's Law; Critical point; Fluctuations; Power-law
distributions; Search engines; Statistics of natural
numbers; The World Wide Web",
}
@Article{Duranton:2006:SFZ,
author = "Gilles Duranton",
title = "Some foundations for {Zipf}'s law: Product
proliferation and local spillovers",
journal = j-REG-SCI-URBAN-ECON,
volume = "36",
number = "4",
pages = "542--563",
day = "1",
month = jul,
year = "2006",
CODEN = "RSUEDM",
DOI = "http://dx.doi.org/10.1016/j.regsciurbeco.2006.03.008",
ISSN = "0166-0462 (print), 1879-2308 (electronic)",
ISSN-L = "0166-0462",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0166046206000354",
acknowledgement = ack-nhfb,
fjournal = "Regional Science and Urban Economics",
journal-URL = "http://www.sciencedirect.com/science/journal/01660462",
keywords = "Zipf's Law",
}
@Article{Egghe:2006:DHL,
author = "L. Egghe",
title = "The dependence of the height of a {Lorenz} curve of a
{Zipf} function on the size of the system",
journal = j-MATH-COMP-MODELLING,
volume = "43",
number = "7--8",
pages = "870--879",
day = "15",
month = apr,
year = "2006",
CODEN = "MCMOEG",
DOI = "http://dx.doi.org/10.1016/j.mcm.2005.09.033",
ISSN = "0895-7177 (print), 1872-9479 (electronic)",
ISSN-L = "0895-7177",
MRclass = "94A15 (91B82)",
MRnumber = "2218323 (2006k:94033)",
MRreviewer = "Ulrich Tamm",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S089571770500508X",
acknowledgement = ack-nhfb,
fjournal = "Mathematical and Computer Modelling",
keywords = "Zipf's Law",
}
@Article{Gaite:2006:CSZ,
author = "Jos{\'e} Gaite",
title = "Cut-out sets and the {Zipf} law for fractal voids",
journal = j-PHYSICA-D,
volume = "223",
number = "2",
pages = "248--255",
day = "15",
month = nov,
year = "2006",
CODEN = "PDNPDT",
DOI = "http://dx.doi.org/10.1016/j.physd.2006.09.021",
ISSN = "0167-2789 (print), 1872-8022 (electronic)",
ISSN-L = "0167-2789",
MRclass = "28A80",
MRnumber = "2307212",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167278906003848",
acknowledgement = ack-nhfb,
fjournal = "Physica. D, Nonlinear phenomena",
keywords = "Zipf's Law",
}
@Article{Gan:2006:ZLS,
author = "Li Gan and Dong Li and Shunfeng Song",
title = "Is the {Zipf} law spurious in explaining city-size
distributions?",
journal = j-ECONOM-LETT,
volume = "92",
number = "2",
pages = "256--262",
day = "1",
month = aug,
year = "2006",
CODEN = "ECLEDS",
DOI = "http://dx.doi.org/10.1016/j.econlet.2006.03.004",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165176506000772",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
keywords = "Zipf's Law",
}
@Article{Handurukande:2006:PSB,
author = "S. B. Handurukande and A.-M. Kermarrec and F. {Le
Fessant} and L. Massouli{\'e} and S. Patarin",
title = "Peer sharing behaviour in the {eDonkey} network, and
implications for the design of server-less file sharing
systems",
journal = j-OPER-SYS-REV,
volume = "40",
number = "4",
pages = "359--371",
month = oct,
year = "2006",
CODEN = "OSRED8",
DOI = "http://doi.acm.org/10.1145/1218063.1217970",
ISSN = "0163-5980 (print), 1943-586X (electronic)",
ISSN-L = "0163-5980",
bibdate = "Fri Jun 20 17:14:10 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "In this paper we present an empirical study of a
workload gathered by crawling the eDonkey network --- a
dominant peer-to-peer file sharing system --- for over
50 days. We first confirm the presence of some known
features, in particular the prevalence of free-riding
and the Zipf-like distribution of file popularity. We
also analyze the evolution of document popularity. We
then provide an in-depth analysis of several clustering
properties of such workloads. We measure the
geographical clustering of peers offering a given file.
We find that most files are offered mostly by peers of
a single country, although popular files don't have
such a clear home country. We then analyze the overlap
between contents offered by different peers. We find
that peer contents are highly clustered according to
several metrics of interest. We propose to leverage
this property by allowing peers to search for content
without server support, by querying suitably identified
semantic neighbours. We find via trace-driven
simulations that this approach is generally effective,
and is even more effective for rare files. If we
further allow peers to query both their semantic
neighbours, and in turn their neighbours' neighbours,
we attain hit rates as high as over 55\% for neighbour
lists of size 20.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGOPS Operating Systems Review",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J597",
keywords = "file sharing; peer-to-peer; simulation; trace",
}
@InCollection{Harremoes:2006:ZLH,
author = "P. Harremo{\"e}s and F. Topsoe",
editor = "Rudolf Ahlswede and others",
booktitle = "General theory of information transfer and
combinatorics",
title = "{Zipf}'s law, hyperbolic distributions and entropy
loss",
volume = "4123",
publisher = pub-SV,
address = pub-SV:adr,
pages = "788--792",
year = "2006",
DOI = "http://dx.doi.org/10.1007/11889342_50",
bibdate = "Sat Nov 12 11:15:28 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
ZMnumber = "1158.91481",
abstract = "Zipf's law --- or Estoup-Zipf's law --- is an
empirical fact of computational linguistics which
relates rank and frequency of words in natural
languages. The law suggests modelling by distributions
of ``hyperbolic type''. We present a satisfactory
general definition and an information-theoretical
characterization of the resulting hyperbolic
distributions. When applied to linguistics this leads
to a property of stability and flexibility, explaining
that a language can develop towards higher and higher
expressive powers without changing its basic
structure.",
acknowledgement = ack-nhfb,
classmath = "91F20 (Linguistics) 94A15 (General topics of
information theory) 94A17 (Measures of information)",
keywords = "entropy loss; hyperbolic distributions; Zipf's law",
}
@TechReport{Humenberger:2006:BGV,
author = "Hans Humenberger",
title = "{Das ,,Benford-Gesetz'' {\"u}ber die Verteilung der
ersten Ziffer von Zahn}. ({German}) [{Benford}'s Law on
the distribution of the first digit of numbers]",
type = "Report",
institution = "Institut f{\"u}r Mathematik und Angewandte Statistik,
Universit{\"a}t f{\"u}r Bodenkultur",
address = "Gregor Mendel-Stra{\ss}e 33, A-1180, Wien, Austria",
month = aug,
year = "2006",
bibdate = "Sun Feb 17 09:37:40 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.mathematik.uni-kassel.de/didaktik/HomePersonal/fischer/StochScan/1996-3_Hum.pdf",
acknowledgement = ack-nhfb,
language = "German",
}
@TechReport{Hurlimann:2006:BLB,
author = "Werner H{\"u}rlimann",
title = "{Benford's Law} from 1881 to 2006: a bibliography",
type = "Report",
address = "Feldstrasse 145, CH-8004 Z{\"u}rich, Switzerland",
pages = "15",
day = "5",
month = jul,
year = "2006",
bibdate = "Fri Mar 30 11:32:30 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/pdf/math.ST/0607168",
abstract = "On the occasion of the 125-th anniversary of Newcomb's
paper, a bibliography of academic work related to
Benford's law from its year of origin 1881 to 2006 has
been compiled.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "This bibliography lists 325 references on the title
subject, with these (years) and counts: (1881) 1,
(1912) 1, (1916) 1, (1917) 1, (1936) 1, (1938) 1,
(1944) 1, (1945) 1, (1948) 2, (1950) 1, (1952) 1,
(1953) 1, (1954) 1, (1957) 3, (1960) 1, (1961) 2,
(1963) 1, (1964) 2, (1965) 2, (1966) 1, (1967) 1,
(1968) 2, (1969) 5, (1970) 1, (1971) 4, (1972) 2,
(1973) 7, (1974) 2, (1975) 1, (1976) 5, (1977) 3,
(1978) 3, (1979) 2, (1981) 6, (1982) 3, (1983) 4,
(1984) 7, (1985) 2, (1986) 7, (1987) 5, (1988) 1,
(1988) 5, (1989) 2, (1990) 1, (1991) 4, (1992) 6,
(1993) 5, (1994) 5, (1995) 1, (1995) 2, (1996) 4,
(1997) 1, (1997) 9, (1998) 1, (1998) 6, (1999) 12,
(2000) 10, (2001) 19, (2002) 30, (2003) 22, (2004) 29,
(2005) 34, (2006) 18.",
}
@Article{Hurlimann:2006:GBL,
author = "W. Hurlimann",
title = "Generalizing {Benford}'s law using power laws:
application to integer sequences",
journal = "ArXiv Mathematics e-prints",
month = jul,
year = "2006",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2006math......7166H",
acknowledgement = ack-nhfb,
eprint = "arXiv:math/0607166",
keywords = "Mathematics - Statistics, Mathematics - Number Theory,
11B73, 11B83, 11K31, 62E15, 62E17",
}
@Article{Izsak:2006:MLE,
author = "F. Izs{\'a}k",
title = "Maximum likelihood estimation for constrained
parameters of multinomial distributions --- Application
to {Zipf--Mandelbrot} models",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "51",
number = "3",
pages = "1575--1583",
day = "1",
month = dec,
year = "2006",
CODEN = "CSDADW",
DOI = "http://dx.doi.org/10.1016/j.csda.2006.05.008",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
MRnumber = "2307527",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S016794730600154X",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
keywords = "Zipf's Law",
}
@TechReport{Judge:2006:DPS,
author = "George Judge and Laura Schechter",
title = "Detecting problems in survey data using {Benford}'s
law",
type = "Preprint",
institution = "University of California at Berkeley and University of
Wisconsin at Madison",
address = "Berkeley, CA, USA and Madison, WI, USA",
pages = "30",
day = "1",
month = nov,
year = "2006",
bibdate = "Sat Feb 16 18:12:29 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.aae.wisc.edu/lschechter/benford.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Kossovsky:2006:TBU,
author = "Alex Ely Kossovsky",
title = "Towards a Better Understanding of the Leading Digits
Phenomena",
journal = "ArXiv Mathematics e-prints",
year = "2006",
bibdate = "Mon Nov 21 06:46:43 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/math/0612627",
abstract = "This article on leading digits (Benford's Law)
contains the following: (i) An attempt at a
comprehensive account on the leading digits phenomena,
incorporating many of its existing explanations,
proofs, and differing points of view. (ii) The finding
that leading digits of random numbers derived from a
chain of distributions that are linked via parameter
selection are logarithmic in the limit as the number of
sequences approaches infinity, and that empirically
only around 5 or 6 sequences of such a distribution
chain are needed to obtain results that are close
enough to the logarithmic (i.e., rapid convergence).
(iii) An outright exact logarithmic behavior for a
2-sequence chain whenever parametrical density is
exactly logarithmic. (iv) An account on the existence
of singularities in exponential growth rates with
regards to the leading digits distributions of their
series. (v) An account on several distributions that
are intrinsically logarithmic or approximately so. (vi)
A conceptual justification of Flehinger's iterated
averaging scheme --- an algorithm that was presented
without any clear motivation. (vii) A note on the close
relationship of Flehinger's scheme and the chain of
distribution to Hill's super distribution. (viii) A
conceptual argument justifying the scale invariance
principle --- a principle invoked in derivations of
Benford's law. (ix) A note on the intimate connection
between one-sided tail to the right in density
distributions and logarithmic leading digit behavior.",
acknowledgement = ack-nhfb,
remark = "On 18 February 2013, the archive has 17 revisions of
this article.",
xxjournal = "CoRR",
}
@Article{Kristiansen:2006:BTZ,
author = "K. de Lange Kristiansen and G. Helgesen and A. T.
Skjeltorp",
title = "Braid theory and {Zipf--Mandelbrot} relation used in
microparticle dynamics",
journal = j-EUR-PHYS-J-B,
volume = "51",
number = "3",
pages = "363--371",
month = jun,
year = "2006",
CODEN = "EPJBFY",
DOI = "http://dx.doi.org/10.1140/epjb/e2006-00241-7",
ISSN = "1434-6028 (print), 1434-6036 (electronic)",
ISSN-L = "1434-6028",
bibdate = "Sat Sep 8 18:31:14 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "European Physical Journal B: Condensed Matter and
Complex Systems",
journal-URL = "http://link.springer.com/journal/10051",
}
@Book{Kuipers:2006:UDS,
author = "Lauwerens Kuipers and Harald Niederreiter",
title = "Uniform distribution of sequences",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xviii + 390",
year = "2006",
ISBN = "0-486-45019-8 (paperback)",
ISBN-13 = "978-0-486-45019-3 (paperback)",
LCCN = "QA292 .K84 2006",
bibdate = "Sat Nov 12 15:42:53 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0625/2005056064-d.html;
http://www.loc.gov/catdir/toc/fy0612/2005056064.html",
acknowledgement = ack-nhfb,
remark = "Originally published in \cite{Kuipers:1974:UDS}.",
subject = "Sequences (Mathematics); Uniform distribution
(Probability theory)",
}
@Article{Kulikova:2006:HFD,
author = "A. A. Kulikova and Yu. V. Prokhorov and V. I.
Khokhlov",
title = "{H.F.D.} ({$H$}-function Distribution) and {Benford's
Law}. {I}",
journal = j-THEORY-PROBAB-APPL,
volume = "50",
number = "2",
pages = "311--315",
month = jan,
year = "2006",
CODEN = "TPRBAU",
DOI = "http://dx.doi.org/10.1137/S0040585X97981706",
ISSN = "0040-585X (print), 1095-7219 (electronic)",
ISSN-L = "0040-585X",
bibdate = "Wed May 19 18:14:51 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/50/2;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://epubs.siam.org/tvp/resource/1/tprbau/v50/i2/p311_s1",
acknowledgement = ack-nhfb,
fjournal = "Theory of probability and its applications",
journal-URL = "http://epubs.siam.org/tvp",
}
@Article{Lagarias:2006:BLF,
author = "Jeffrey C. Lagarias and K. Soundararajan",
title = "{Benford}'s law for the $ 3 x + 1 $ function",
journal = "J. London Math. Soc. (2)",
volume = "74",
number = "2",
pages = "289--303",
year = "2006",
CODEN = "JLMSAK",
DOI = "http://dx.doi.org/10.1112/S0024610706023131",
ISSN = "0024-6107 (print), 1469-7750 (electronic)",
ISSN-L = "0024-6107",
MRclass = "37A45",
MRnumber = "2269630 (2007h:37007)",
MRreviewer = "Radhakrishnan Nair",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the London Mathematical Society. Second
Series",
}
@Article{Leinicke:2006:FFN,
author = "Linda M. Leinicke and Joyce A. Ostrosky and W. Max
Rexroad",
title = "Fighting fraud by the numbers: Digital analysis
primer",
journal = "Fraud Magazine",
volume = "??",
number = "??",
pages = "??--??",
month = jan # "\slash " # feb,
year = "2006",
ISSN = "1553-6645",
ISSN-L = "1553-6645",
bibdate = "Sun Feb 17 08:13:02 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.fraud-magazine.com/article.aspx?id=4294967620",
acknowledgement = ack-nhfb,
fjournal = "Fraud Magazine. {A} Publication of the Association of
Certified Fraud Examiners",
keywords = "Benford's Law",
}
@Article{Leydesdorff:2006:CPL,
author = "Loet Leydesdorff and Stephen Bensman",
title = "Classification and power laws: the logarithmic
transformation",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "57",
number = "11",
pages = "1470--1486",
month = sep,
year = "2006",
CODEN = "JASIEF",
DOI = "http://dx.doi.org/10.1002/asi.20467",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Sat Feb 16 18:31:04 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
keywords = "Benford's Law",
}
@Article{Lim:2006:BRB,
author = "Nena Lim",
title = "Book Review: {{\booktitle{The new forensics:
investigating corporate fraud and the theft of
intellectual property}}, J. Anastasi. John Wiley \&
Sons, New Jersey (2003)}",
journal = "Digital Investigation",
volume = "3",
number = "4",
pages = "245--246",
year = "2006",
DOI = "http://dx.doi.org/10.1016/j.diin.2006.10.002",
ISSN = "1742-2876",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S174228760600106X",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@InCollection{Lu:2006:AFD,
author = "Fletcher Lu and J. Efrim Boritz and Dominic Covvey",
booktitle = "Advances in artificial intelligence",
title = "Adaptive fraud detection using {Benford}'s law",
volume = "4013",
publisher = pub-SV,
address = pub-SV:adr,
pages = "347--358",
year = "2006",
DOI = "http://dx.doi.org/10.1007/11766247_30",
MRnumber = "2280590",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@InProceedings{Lu:2006:BCF,
author = "F. Lu and J. E. Boritz",
editor = "????",
booktitle = "{Uncertainty in Artificial Intelligence: Proceedings
of the 22nd Conference}",
title = "Building a case for fraud using {Benford}'s law with
reinforcement learning",
publisher = "????",
address = "????",
pages = "??--??",
year = "2006",
bibdate = "Sat Feb 16 18:34:47 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Manaris:2006:IES,
author = "Bill Manaris and Luca Pellicoro and George Pothering
and Harland Hodges",
editor = "????",
booktitle = "{2006 IASTED International Conference on Artificial
Intelligence and Applications (AIA 2006), February
13--16, 2006, Innsbruck, Austria}",
title = "Investigating {Esperanto}'s statistical proportions
relative to other languages using neural networks and
{Zipf}'s law",
publisher = "Acta Press",
address = "????",
pages = "1--7",
year = "2006",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 18:41:37 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.cs.cofc.edu/~manaris/uploads/Main/IASTED2006.pdf",
acknowledgement = ack-nhfb,
}
@Article{Marchi:2006:AAS,
author = "Scott Marchi and James Hamilton",
title = "Assessing the Accuracy of Self-Reported Data: an
Evaluation of the Toxics Release Inventory",
journal = "Journal of Risk and Uncertainty",
volume = "32",
number = "1",
pages = "57--76",
month = jan,
year = "2006",
CODEN = "JRUNEN",
DOI = "http://dx.doi.org/10.1007/s10797-006-6666-3",
ISSN = "0895-5646 (print), 1573-0476 (electronic)",
ISSN-L = "0895-5646",
bibdate = "Fri Nov 25 11:25:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Maslov:2006:BGA,
author = "V. P. Maslov",
title = "{Bose} gas of anharmonic oscillators and a refinement
of {Zipf}'s law",
journal = j-TEORET-MATH-FIZ,
volume = "148",
number = "3",
pages = "495--496",
year = "2006",
CODEN = "TMFZAL",
DOI = "http://dx.doi.org/10.1007/s11232-006-0117-2",
ISSN = "0564-6162",
ISSN-L = "0564-6162",
MRclass = "82B10",
MRnumber = "2283664",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
Matematicheskaya Fizika",
}
@Article{Maslov:2006:NAD,
author = "V. P. Maslov",
title = "Negative asymptotic dimension, a new condensate, and
their relation to the quantized {Zipf} law",
journal = j-MAT-ZAMETKI,
volume = "80",
number = "6",
pages = "856--863",
year = "2006",
CODEN = "????",
DOI = "http://dx.doi.org/10.1007/s11006-006-0203-7",
ISSN = "0025-567X",
ISSN-L = "0025-567X",
MRclass = "82B10 (20F69 53C23 81S10 91F20)",
MRnumber = "2311613 (2008e:82005)",
MRreviewer = "Artur E. Ruuge",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
Zametki",
}
@Article{Maslov:2006:RZM,
author = "V. P. Maslov",
title = "A refinement of the {Zipf--Mandelbrot} law and
lacunarity in an ideal gas",
journal = j-TEORET-MATH-FIZ,
volume = "147",
number = "3",
pages = "511--512",
year = "2006",
CODEN = "TMFZAL",
DOI = "http://dx.doi.org/10.1007/s11232-006-0083-8",
ISSN = "0564-6162",
ISSN-L = "0564-6162",
MRclass = "82B10",
MRnumber = "2254729 (2007d:82007)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
Matematicheskaya Fizika",
}
@Article{Maslov:2006:ZLR,
author = "V. P. Maslov and T. V. Maslova",
title = "On {Zipf}'s law and rank distributions in linguistics
and semiotics",
journal = j-MAT-ZAMETKI,
volume = "80",
number = "5",
pages = "718--732",
year = "2006",
CODEN = "????",
DOI = "http://dx.doi.org/10.1007/s11006-006-0189-1",
ISSN = "0025-567X",
ISSN-L = "0025-567X",
MRclass = "60C05 (62-07 62P99)",
MRnumber = "2311586 (2008g:60027)",
MRreviewer = "Konstantin E. Feldman",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "Zbl 1134.62086",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
Zametki",
}
@Article{Maslova:2006:ZLM,
author = "T. V. Maslova",
title = "{Zipf}'s law and {Maslov}'s formula as applied to
semiotic systems",
journal = j-DOKL-MATH,
volume = "74",
number = "3",
pages = "917--920",
year = "2006",
CODEN = "????",
DOI = "http://dx.doi.org/10.1134/S1064562406060330",
ISSN = "1064-5624 (print), 1531-8362 (electronic)",
ISSN-L = "1064-5624",
bibdate = "Sat Nov 12 11:13:35 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "pre05824774",
acknowledgement = ack-nhfb,
classmath = "62E20 (Asymptotic distribution theory in statistics)
82B03 (Foundations of equilibrium statistical
mechanics)",
fjournal = "Doklady Mathematics",
language = "English. Russian original",
}
@Article{Maslova:2006:ZLV,
author = "T. V. Maslova",
title = "On the {Zipf} law and the {V. P. Maslov} formula for
semiotic systems",
journal = j-DOKL-AKAD-NAUK,
volume = "411",
number = "6",
pages = "754--757",
year = "2006",
CODEN = "DANKAS",
ISSN = "0869-5652",
ISSN-L = "0869-5652",
MRclass = "62E20 (82B03)",
MRnumber = "2451374",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii
Nauk",
}
@InProceedings{Mebane:2006:DAE,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{2006 Annual Meeting of the Midwest Political Science
Association, April 20--23, Palmer House, Chicago}",
title = "Detecting Attempted Election Theft: Vote Counts,
Voting Machines and {Benford's Law}",
publisher = "????",
address = "????",
pages = "i + 50",
day = "19",
month = apr,
year = "2006",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 12:14:14 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.umich.edu/~wmebane/mw06.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Mebane:2006:EFS,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{Election Fraud Conference, Salt Lake City, Utah,
September 29--30, 2006}",
title = "Election Forensics: The Second-digit {Benford's Law}
Test and Recent {American Presidential} Elections",
publisher = "????",
address = "????",
pages = "??--??",
year = "2006",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Feb 15 18:22:27 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www-personal.umich.edu/~wmebane/fraud06.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Mebane:2006:EFV,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{2006 Summer Meeting of the Political Methodology
Society, UC-Davis, July 20--22, 2006}",
title = "Election Forensics: Vote Counts and {Benford's Law}",
publisher = "????",
address = "????",
pages = "ii + 48",
day = "18",
month = jul,
year = "2006",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 12:01:26 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.umich.edu/~wmebane/pm06.pdf",
acknowledgement = ack-nhfb,
}
@Article{Mellor:2006:GKZ,
author = "Andy Mellor",
title = "Book Review: {G. K. Zipf, \booktitle The
Psycho-biology of Language (1935) MIT Press, Cambridge,
MA}",
journal = j-SYSTEM,
volume = "34",
number = "3",
pages = "455--457",
day = "20",
month = sep,
year = "2006",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/j.system.2006.07.004",
ISSN = "0346-251X (print), 1879-3282 (electronic)",
ISSN-L = "0346-251X",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0346251X06000674",
acknowledgement = ack-nhfb,
fjournal = "System",
journal-URL = "http://www.sciencedirect.com/science/journal/0346251X",
keywords = "Zipf's Law",
}
@Article{Metwally:2006:IES,
author = "Ahmed Metwally and Divyakant Agrawal and Amr {El
Abbadi}",
title = "An integrated efficient solution for computing
frequent and top-$k$ elements in data streams",
journal = j-TODS,
volume = "31",
number = "3",
pages = "1095--1133",
month = sep,
year = "2006",
CODEN = "ATDSD3",
DOI = "http://doi.acm.org/10.1145/1166074.1166084",
ISSN = "0362-5915 (print), 1557-4644 (electronic)",
ISSN-L = "0362-5915",
bibdate = "Tue Oct 17 05:41:01 MDT 2006",
bibsource = "http://www.acm.org/pubs/contents/journals/tods/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See comments in \cite{Liu:2010:CIE}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Database Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777",
}
@Book{Miller:2006:IMN,
author = "Steven J. Miller and Ramin Takloo-Bighash",
title = "An Invitation to Modern Number Theory",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xx + 503",
year = "2006",
ISBN = "0-691-12060-9 (hardcover)",
ISBN-13 = "978-0-691-12060-7 (hardcover)",
LCCN = "QA241 .M5344 2006",
bibdate = "Fri Mar 22 08:57:57 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
subject = "Number theory",
tableofcontents = "Part 1. Basic Number Theory \\
1. Mod p Arithmetic, Group Theory and Cryptography \\
2. Arithmetic Functions \\
3. Zeta and L-Functions \\
4. Solutions to Diophantine Equations \\
Part 2. Continued Fractions and Approximations \\
5. Algebraic and Transcendental Numbers \\
6. The Proof of Roth's Theorem \\
7. Introduction to Continued Fractions \\
Part 3. Probabilistic Methods and Equidistribution \\
8. Introduction to Probability \\
9. Applications of Probability: Benford's Law and
Hypothesis Testing \\
10. Distribution of Digits of Continued Fractions \\
11. Introduction to Fourier Analysis \\
12. f n k g and Poissonian Behavior \\
Part 4. The Circle Method \\
13. Introduction to the Circle Method \\
14. Circle Method: Heuristics for Germain Primes \\
Part 5. Random Matrix Theory and L-Functions \\
15. From Nuclear Physics to L-Functions \\
16. Random Matrix Theory: Eigenvalue Densities \\
17. Random Matrix Theory: Spacings between Adjacent
Eigenvalues \\
18. The Explicit Formula and Density Conjectures \\
Appendix A. Analysis Review \\
Appendix B. Linear Algebra Review \\
Appendix C. Hints and Remarks on the Exercises \\
Appendix D. Concluding Remarks",
}
@Article{Miller:2006:MCL,
author = "S. J. Miller and M. J. Nigrini",
title = "The {Modulo 1 Central Limit Theorem} and {Benford's
Law} for Products",
journal = "International Journal of Algebra",
volume = "3",
number = "3",
pages = "119--130",
month = jul,
year = "2006",
CODEN = "????",
ISSN = "1312-8868",
ISSN-L = "1312-8868",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2006math......7686M;
http://arxiv.org/abs/math/0607686",
abstract = "We derive a necessary and sufficient condition for the
sum of $M$ independent continuous random variables
modulo $1$ to converge to the uniform distribution in $
L^1 ([0, 1]) $, and discuss generalizations to discrete
random variables. A consequence is that if $ X_1,
\ldots {}, X_M $ are independent continuous random
variables with densities $ f_1, \ldots {}, f_M $, for
any base $B$ as $ M \to \infty $ for many choices of
the densities the distribution of the digits of $ X_1 *
\cdots {} * X_M $ converges to Benford's law base $B$.
The rate of convergence can be quantified in terms of
the Fourier coefficients of the densities, and provides
an explanation for the prevalence of Benford behavior
in many diverse systems.",
acknowledgement = ack-nhfb,
eprint = "arXiv:math/0607686",
keywords = "Mathematics - Probability, Mathematics - Classical
Analysis and ODEs, 60F05, 60F25, 11K06 (Primary),
42A10, 42A61, 62E15 (Secondary)",
}
@Article{Miller:2006:OSB,
author = "S. J. Miller and M. J. Nigrini",
title = "Order Statistics and {Benford's Law}",
journal = "ArXiv Mathematics e-prints",
month = jan,
year = "2006",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2006math......1344M",
acknowledgement = ack-nhfb,
eprint = "arXiv:math/0601344",
keywords = "Mathematics - Probability, Mathematics - Number
Theory, 11K06, 60A10 (Primary), 46F12, 60F05, 42A16
(Secondary)",
}
@Article{Moret:2006:NBL,
author = "M. A. Moret and V. de Senna and M. G. Pereira and G.
F. Zebende",
title = "{Newcomb--Benford} Law in Astrophysical Sources",
journal = j-INT-J-MOD-PHYS-C,
volume = "17",
number = "11",
pages = "1597--1604",
month = "????",
year = "2006",
CODEN = "IJMPEO",
ISSN = "0129-1831 (print), 1793-6586 (electronic)",
ISSN-L = "0129-1831",
bibdate = "Mon Nov 14 17:37:59 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2006IJMPC..17.1597M",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Modern Physics C [Physics and
Computers]",
journal-URL = "http://www.worldscientific.com/loi/ijmpc",
}
@TechReport{Morrow:2006:BLF,
author = "John Morrow",
title = "{Benford's Law}, Families of Distributions and a Test
Basis",
type = "Report",
institution = "University of Wisconsin--Madison",
address = "Madison, WI, USA",
month = "????",
year = "2006",
bibdate = "Tue Nov 22 20:44:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Revised draft of 9 October 2010.",
URL = "http://www.johnmorrow.info/projects/benford/benfordMain.pdf",
acknowledgement = ack-nhfb,
lastaccess = "22 November 2011",
}
@Article{Moura:2006:ZLB,
author = "Newton J. Moura Jr. and Marcelo B. Ribeiro",
title = "{Zipf} law for {Brazilian} cities",
journal = j-J-THEOR-BIOL,
volume = "219",
number = "4",
pages = "441--448",
day = "15",
month = jul,
year = "2006",
CODEN = "JTBIAP",
DOI = "http://dx.doi.org/10.1016/j.physa.2005.11.038",
ISSN = "0022-5193 (print), 1095-8541 (electronic)",
ISSN-L = "0022-5193",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437105012422",
acknowledgement = ack-nhfb,
fjournal = "Journal of Theoretical Biology",
journal-URL = "http://www.sciencedirect.com/science/journal/00225193",
keywords = "Zipf's Law",
}
@TechReport{Nigrini:2006:BLA,
author = "M. J. Nigrini and S. J. Miller",
title = "{Benford}'s law applied to hydrology data --- results
and relevance to other geophysical data",
type = "Preprint",
institution = "????",
address = "????",
month = "????",
year = "2006",
bibdate = "Sat Feb 16 18:58:34 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Ogasawara:2006:ZLH,
author = "Osamu Ogasawara and Shoko Kawamoto and Kousaku Okubo",
title = "{Zipf}'s law and human transcriptomes: an explanation
with an evolutionary model",
journal = j-C-R-BIOL,
volume = "326",
number = "10--11",
pages = "1097--1101",
day = "1",
month = jul,
year = "2006",
CODEN = "CRBOCM",
DOI = "http://dx.doi.org/10.1016/j.crvi.2003.09.031",
ISSN = "1631-0691 (print), 1768-3238 (electronic)",
ISSN-L = "1631-0691",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1631069103002294",
acknowledgement = ack-nhfb,
fjournal = "Comptes Rendus Biologies",
journal-URL = "http://sciencedirect.com/science/journal/16310691",
keywords = "Zipf's Law",
}
@Article{Pocheau:2006:SDL,
author = "A. Pocheau",
title = "The significant digit law: a paradigm of statistical
scale symmetries",
journal = j-EUR-PHYS-J-B,
volume = "49",
number = "4",
pages = "491--511",
month = feb,
year = "2006",
CODEN = "EPJBFY",
DOI = "http://dx.doi.org/10.1140/epjb/e2006-00084-2",
ISSN = "1434-6028 (print), 1434-6036 (electronic)",
ISSN-L = "1434-6028",
bibdate = "Sat Feb 16 15:06:20 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1140/epjb/e2006-00084-2",
acknowledgement = ack-nhfb,
fjournal = "European Physical Journal B: Condensed Matter and
Complex Systems",
journal-URL = "http://link.springer.com/journal/10051",
}
@Article{Posch:2006:ADP,
author = "Peter N. Posch and Welf A. Kreiner",
title = "Analysing digits for portfolio formation and index
tracking",
journal = j-J-ASSET-MANAGE,
volume = "7",
number = "1",
pages = "69--80",
month = may,
year = "2006",
CODEN = "????",
DOI = "http://dx.doi.org/10.1057/palgrave.jam.2240203",
ISSN = "1470-8272 (print), 1479-179X (electronic)",
ISSN-L = "1470-8272",
bibdate = "Fri Nov 25 11:19:38 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "A general methodology is proposed for using digit
distributions as an approach to examining arbitrary
datasets. With the Newcomb--Benford law as a starting
point, a more general framework for digital analysis is
developed. A new measure is proposed based on this
framework, namely the Digital-Fit Factor (DFF). The use
of index comparison on the S\&P500 and the Dow Jones
Industrial Average is demonstrated. The DFF is then
used to construct portfolios and measure their
performance compared with that of the index. The
average returns using the measure exceed the index
composition by 6--14 percentage points per year by
being more stable at the same time. Furthermore, these
measures require only a very small proportion of the
available information and are thus very efficient.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Asset Management",
keywords = "Benford's Law",
}
@Article{Ree:2006:PLD,
author = "Suhan Ree",
title = "Power-law distributions from additive preferential
redistributions",
journal = j-PHYS-REV-E,
volume = "73",
number = "??",
pages = "026115",
day = "15",
month = feb,
year = "2006",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.73.026115",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.73.026115",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@InProceedings{Sanches:2006:IRU,
author = "Jo{\~a}o M. Sanches and Jorge S. Marques",
booktitle = "{2006 IEEE International Conference on Image
Processing, Atlanta, Georgia, 8--11 October 2006}",
title = "Image Reconstruction using the {Benford Law}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2029--2032",
year = "2006",
DOI = "http://dx.doi.org/10.1109/ICIP.2006.312845",
ISBN = "1-4244-0480-0",
ISBN-13 = "978-1-4244-0480-3",
ISSN = "1522-4880",
bibdate = "Tue Nov 15 09:03:24 2011",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/icip/icip2006.html#SanchesM06;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Tt has been claimed that the first digit of real
signals follows a logarithmic distribution, called
Benford law. This paper shows that this distribution is
a natural prior for the gradient of several types of
medical images (MRI, CT, ultrasound) and proposes a
reconstruction algorithm based on the Benford law which
does not require any parameter tuning. Experimental
results are presented to illustrate the performance of
the reconstruction algorithm",
acknowledgement = ack-nhfb,
}
@Article{Savile:2006:UBL,
author = "A. Savile",
title = "Using {Benford's} Law to detect data error and fraud:
An examination of companies listed on the {Johannesburg
Stock Exchange}",
journal = "South African Journal of Economic and Management
Sciences",
volume = "9",
number = "3",
pages = "341--354",
month = "????",
year = "2006",
CODEN = "????",
ISSN = "1015-8812 (print), 2222-3436 (electronic)",
ISSN-L = "1015-8812",
bibdate = "Fri Mar 22 09:12:15 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
journal-URL = "http://sajems.org/index.php/sajems/issue/archive",
keywords = "Benford's Law",
remark = "No issues online before volume 10, number 1, 2007.",
}
@Article{Schneider:2006:RAS,
author = "Reto U. Schneider",
title = "{Das R{\"a}tsel der abgegriffenen Seiten: Vor {\"u}ber
hundert Jahren stiess ein Astronom auf ein
merkw{\"u}rdiges statistisches Gesetz, das heute
Steuerbetr{\"u}ger entlarven soll}. ({German}) [{The}
puzzle of the worn pages: More than a hundred years ago
an astronomer came across a strange statistical law
that will now expose tax cheats]",
journal = "{NZZ Folio: Die Zeitschrift der Neuen Z{\"u}rcher
Zeitung}",
number = "1/06",
month = "????",
year = "2006",
bibdate = "Fri Nov 18 12:18:17 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www-x.nzz.ch/folio/curr/articles/schneider_2.html;
http://www.nzzfolio.ch/www/d80bd71b-b264-4db4-afd0-277884b93470/showarticle/4c9a5444-883e-4e6b-8a4c-6c31f32c02f3.aspx",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Schuette:2006:TFZ,
author = "Paul Schuette and Marcus C. Spruill",
title = "Tail fit and the {Zipf--Pareto} law",
journal = "Extremes",
volume = "9",
number = "3--4",
pages = "243--261",
year = "2006",
CODEN = "????",
DOI = "http://dx.doi.org/10.1007/s10687-007-0030-6",
ISSN = "1386-1999",
ISSN-L = "1386-1999",
MRnumber = "2367837",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Extremes. Statistical Theory and Applications in
Science, Engineering and Economics",
xxyear = "2007",
}
@Article{Sugimoto:2006:AFP,
author = "Toyoaki Sugimoto and Naoto Miyoshi",
title = "On the asymptotics of fault probability in
least-recently-used caching with {Zipf}-type request
distribution",
journal = j-RAND-STRUCT,
volume = "29",
number = "3",
pages = "296--323",
year = "2006",
CODEN = "RSALFD",
DOI = "http://dx.doi.org/10.1002/rsa.20098",
ISSN = "1042-9832",
ISSN-L = "1042-9832",
MRclass = "68N25 (60C05 62E20 62P30 68P05 68U35)",
MRnumber = "2254493 (2008h:68028)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Random Structures and Algorithms",
keywords = "distributional tail asymptotics; least-recently-used
caching; move-to-front algorithm; negative association;
Zipf-type distribution",
}
@MastersThesis{TorresNunez:2006:NBL,
author = "David A. {Torres N{\'u}{\~n}ez}",
title = "{Newcomb--Benford's Law}: Applications to Electoral
Processes, Bioinformatics, and the Stock Index",
type = "{M.S.} thesis",
school = "Center for Bioststatistics and Bioinformatics,
University of Puerto Rico, R{\'\i}o Piedras Campus",
address = "PO Box 23355, San Juan, PR 00931-3355",
month = may,
year = "2006",
bibdate = "Fri Feb 15 18:34:47 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
advisor = "Luis R{\'a}ul Pericchi Guerra",
}
@Article{VandeWalle:2006:ZGK,
author = "J. {Van de Walle} and K. Willems",
title = "{Zipf, George Kingsley (1902--1950)}",
journal = j-J-ECON-DYN-CONTROL,
volume = "31",
number = "7",
pages = "756--757",
day = "15",
month = jul,
year = "2006",
CODEN = "JEDCDH",
DOI = "http://dx.doi.org/10.1016/B0-08-044854-2/04726-X",
ISSN = "0165-1889 (print), 1879-1743 (electronic)",
ISSN-L = "0165-1889",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/B008044854204726X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Economic Dynamics and Control",
keywords = "Zipf's Law",
}
@Article{Wilkinson:2006:RPC,
author = "Leland Wilkinson",
title = "Revising the {Pareto} Chart",
journal = j-AMER-STAT,
volume = "60",
number = "4",
pages = "332--334",
month = nov,
year = "2006",
CODEN = "ASTAAJ",
DOI = "http://pubs.amstat.org/doi/pdfplus/10.1198/000313006X152243",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Thu Aug 26 21:48:27 MDT 2010",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Ackermann:2007:DMB,
author = "Heiner Ackermann and Alantha Newman and Heiko
R{\"o}glin and Berthold V{\"o}cking",
title = "Decision-making based on approximate and smoothed
{Pareto} curves",
journal = j-THEOR-COMP-SCI,
volume = "378",
number = "3",
pages = "253--270",
day = "9",
month = jun,
year = "2007",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Tue Mar 29 08:55:49 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/science/journal/03043975",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{Amin:2007:TVA,
author = "Zeinab H. Amin",
title = "Tests for the Validity of the Assumption that the
Underlying Distribution of Life is {Pareto}",
journal = j-J-APPL-STAT,
volume = "34",
number = "2",
pages = "195--201",
year = "2007",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Wed Aug 25 11:41:54 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
}
@Misc{Anonymous:2007:ZL,
author = "Anonymous",
key = "Zipf's Law",
title = "{Zipf}'s law",
year = "2007",
bibdate = "Sat Jan 26 12:46:16 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/datacompression.bib",
URL = "http://en.wikipedia.org/wiki/Zipf's_law",
acknowledgement = ack-ds,
lastaccess = "27 January 2013",
rawdata = "Zipf's Law (2007)
|http://en.wikipedia.org/wiki/Zipf's_law|",
}
@Article{Bakulina:2007:AZL,
author = "M. P. Bakulina",
title = "Application of {Zipf}'s law for text compression",
journal = "Diskretn. Anal. Issled. Oper. Ser. 2",
volume = "14",
number = "2",
pages = "3--13",
year = "2007",
CODEN = "????",
ISSN = "1560-9901",
ISSN-L = "1560-9901",
MRclass = "94A15",
MRnumber = "2542308 (2010i:94076)",
MRreviewer = "I. Vajda",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Diskretny{\u\i} Analiz i Issledovanie Operatsi{\u\i}.
Seriya 2",
}
@Article{Baskerville:2007:GAS,
author = "Kim Baskerville and Peter Grassberger and Maya
Paczuski",
title = "Graph animals, subgraph sampling, and motif search in
large networks",
journal = j-PHYS-REV-E,
volume = "76",
number = "??",
pages = "036107",
day = "11",
month = sep,
year = "2007",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.76.036107",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.76.036107",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Benguigui:2007:DMC,
author = "Lucien Benguigui and Efrat Blumenfeld-Lieberthal",
title = "A dynamic model for city size distribution beyond
{Zipf}'s law",
journal = j-PHYSICA-A,
volume = "384",
number = "2",
pages = "613--627",
day = "15",
month = oct,
year = "2007",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2007.05.059",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437107006061",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Article{Berger:2007:DMN,
author = "A. Berger and S. Siegmund",
title = "On the distribution of mantissae in nonautonomous
difference equations",
journal = j-J-DIFFERENCE-EQU-APPL,
volume = "13",
number = "8--9",
pages = "829--845",
month = "????",
year = "2007",
CODEN = "JDEAEA",
DOI = "http://dx.doi.org/10.1080/10236190701388039",
ISSN = "1023-6198 (print), 1563-5120 (electronic)",
ISSN-L = "1023-6198",
MRclass = "37A45 (37B55 39A11)",
MRnumber = "2343033 (2008j:37010)",
MRreviewer = "Reinhard Winkler",
bibdate = "Tue Feb 19 09:37:52 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Second Memorial Issue in Honour of Bernd Aulbach.",
URL = "http://www.math.ualberta.ca/~aberger/benford_bibliography/berger_siegmund_07.pdf",
acknowledgement = ack-nhfb,
fjournal = "Journal of Difference Equations and Applications",
journal-URL = "http://www.informaworld.com/1023-6198",
}
@Article{Berger:2007:NMO,
author = "Arno Berger and Theodore P. Hill",
title = "{Newton}'s Method Obeys {Benford}'s Law",
journal = j-AMER-MATH-MONTHLY,
volume = "114",
number = "7",
pages = "588--601",
month = aug # "\slash " # sep,
year = "2007",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "65G50 (37N30)",
MRnumber = "2341322 (2008h:65016)",
MRreviewer = "Uwe Sch{\"a}fer",
bibdate = "Mon Jan 30 12:00:29 MST 2012",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/i27642270;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/27642274",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Article{Bernik:2007:BLA,
author = "V. I. Bernik and N. I. Kalosha",
title = "{Benford}'s law and the approximation of logarithms of
natural numbers by rational numbers",
journal = "Vests{\=\i} Nats. Akad. Navuk Belarus{\=\i} Ser.
F{\=\i}z.-Mat. Navuk",
volume = "??",
number = "3",
pages = "68--73, 127",
year = "2007",
CODEN = "????",
ISSN = "0002-3574",
ISSN-L = "0002-3574",
MRclass = "11J83 (11A63 11K36)",
MRnumber = "2398318 (2008j:11084)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Vests{\=\i} Natsyyanal\cprime na{\u\i}
Akad{\`e}m{\=\i} {\=\i} Navuk Belarus{\=\i}. Seryya
F{\=\i}z{\=\i}ka-Mat{\`e}matychnykh Navuk. Izvestiya
Natsional\cprime no{\u\i} Akademii Nauk Belarusi.
Seriya Fiziko-Matematicheskikh Nauk. Proceedings of the
National Academy of Sciences of Belarus. Physics and
Mathematics Series",
}
@Article{Brown:2007:UZL,
author = "R. J. C. Brown",
title = "The use of {Zipf}'s law in the screening of analytical
data: a step beyond {Benford}",
journal = j-ANALYST,
volume = "132",
number = "4",
pages = "344",
year = "2007",
CODEN = "ANALAO",
DOI = "http://dx.doi.org/10.1039/b618255k",
ISSN = "0003-2654 (print), 1364-5528 (electronic)",
ISSN-L = "0003-2654",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2007Ana...132..344B",
abstract = "This study shows for the first time the effectiveness
of Zipf's law in screening analytical data sets for
outliers, data formatting and data transcription
errors, particularly when the data sets are small. In
the case of pollutant concentrations in ambient air,
the multivariate nature of the measurement, and the
relationship between the measured values of these
multivariant quantities are the characteristics that
allow a Zipf's law approach to data screening to be
successful. Furthermore, it has been shown that Zipf's
law has advantages over other novel data screening
techniques, such as Benford's law, in terms of
sensitivity and scope",
acknowledgement = ack-nhfb,
fjournal = "The Analyst",
}
@Article{Chacko:2007:EPB,
author = "Manoj Chacko and P. Yageen Thomas",
title = "Estimation of a Parameter of Bivariate {Pareto}
Distribution by Ranked Set Sampling",
journal = j-J-APPL-STAT,
volume = "34",
number = "6",
pages = "703--714",
year = "2007",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Wed Aug 25 11:41:54 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
}
@Article{Cho:2007:BBL,
author = "Wendy K. Tam Cho and Brian J. Gaines",
title = "Breaking the ({Benford}) law: statistical fraud
detection in campaign finance",
journal = j-AMER-STAT,
volume = "61",
number = "3",
pages = "218--223",
month = aug,
year = "2007",
CODEN = "ASTAAJ",
DOI = "http://dx.doi.org/10.1198/000313007X223496",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRnumber = "2393725",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://pubs.amstat.org/doi/pdfplus/10.1198/000313007X223496;
http://www.tandfonline.com/doi/abs/10.1198/000313007X223496",
abstract = "Benford's law is seeing increasing use as a diagnostic
tool for isolating pockets of large datasets with
irregularities that deserve closer inspection. Popular
and academic accounts of campaign finance are rife with
tales of corruption, but the complete dataset of
transactions for federal campaigns is enormous.
Performing a systematic sweep is extremely arduous;
hence, these data are a natural candidate for initial
screening by comparison to Benford's distributions.",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Clauset:2007:FST,
author = "Aaron Clauset and Maxwell Young and Kristian Skrede
Gleditsch",
title = "On the Frequency of Severe Terrorist Events",
journal = j-J-CONFL-RESOLUT,
volume = "51",
number = "1",
pages = "58--87",
month = feb,
year = "2007",
CODEN = "JCFRAL",
DOI = "http://dx.doi.org/10.1177/0022002706296157",
ISSN = "0022-0027 (print), 1552-8766 (electronic)",
ISSN-L = "0022-0027",
bibdate = "Thu Nov 24 14:07:17 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jcr.sagepub.com;
http://jcr.sagepub.com/content/51/1/58.abstract;
http://www.jstor.org/journals/00220027.html",
abstract = "In the spirit of Lewis Richardson's original study of
the statistics of deadly conflicts, we study the
frequency and severity of terrorist attacks worldwide
since 1968. We show that these events are uniformly
characterized by the phenomenon of ``scale
invariance,'' that is, the frequency scales as an
inverse power of the severity, $ P(x) \approx x{-
\alpha } $. We find that this property is a robust
feature of terrorism, persisting when we control for
economic development of the target country, the type of
weapon used, and even for short time scales. Further,
we show that the center of the distribution oscillates
slightly with a period of roughly 13 years, that there
exist significant temporal correlations in the
frequency of severe events, and that current models of
event incidence cannot account for these variations or
the scale invariance property of global terrorism.
Finally, we describe a simple toy model for the
generation of these statistics and briefly discuss its
implications.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Conflict Resolution",
}
@Article{Clauset:2007:PLDa,
author = "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
Newman",
title = "Power-law distributions in empirical data",
journal = "ArXiv Physics e-prints",
day = "7",
month = jun,
year = "2007",
bibdate = "Thu Feb 28 08:52:43 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "arXiv:0706.1062.",
URL = "http://arxiv.org/abs/0706.1062v1",
acknowledgement = ack-nhfb,
pagecount = "27",
}
@Article{Clauset:2007:PLDb,
author = "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
Newman",
title = "Power-law distributions in empirical data",
journal = "ArXiv Physics e-prints",
day = "2",
month = feb,
year = "2009",
DOI = "http://dx.doi.org/10.1137/070710111",
bibdate = "Thu Feb 28 08:52:43 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "arXiv:0706.1062.",
URL = "http://arxiv.org/abs/0706.1062v1",
acknowledgement = ack-nhfb,
pagecount = "43",
}
@Article{Decker:2007:GPC,
author = "Ethan H. Decker and Andrew J. Kerkhoff and Melanie E.
Moses",
title = "Global Patterns of City Size Distributions and Their
Fundamental Drivers",
journal = j-PLOS-ONE,
volume = "2",
number = "9",
pages = "e934",
month = sep,
year = "2007",
CODEN = "POLNCL",
DOI = "http://dx.doi.org/10.1371/journal.pone.0000934",
ISSN = "1932-6203",
bibdate = "Wed Feb 27 06:29:22 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0000934",
abstract = "Urban areas and their voracious appetites are
increasingly dominating the flows of energy and
materials around the globe. Understanding the size
distribution and dynamics of urban areas is vital if we
are to manage their growth and mitigate their negative
impacts on global ecosystems. For over 50 years, city
size distributions have been assumed to universally
follow a power function, and many theories have been
put forth to explain what has become known as Zipf's
law (the instance where the exponent of the power
function equals unity). Most previous studies, however,
only include the largest cities that comprise the tail
of the distribution. Here we show that national,
regional and continental city size distributions,
whether based on census data or inferred from cluster
areas of remotely-sensed nighttime lights, are in fact
lognormally distributed through the majority of cities
and only approach power functions for the largest
cities in the distribution tails. To explore generating
processes, we use a simple model incorporating only two
basic human dynamics, migration and reproduction, that
nonetheless generates distributions very similar to
those found empirically. Our results suggest that
macroscopic patterns of human settlements may be far
more constrained by fundamental ecological principles
than more fine-scale socioeconomic factors.",
acknowledgement = ack-nhfb,
fjournal = "PLoS One",
journal-URL = "http://www.plosone.org/",
keywords = "Zipf's Law",
pagecount = "6",
}
@Article{Diekmann:2007:FDU,
author = "Andreas Diekmann",
title = "Not the First Digit! {Using} {Benford's Law} to Detect
Fraudulent Scientific Data",
journal = j-J-APPL-STAT,
volume = "34",
number = "3--4",
pages = "321--329",
year = "2007",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/02664760601004940",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
MRnumber = "2380543",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
URL = "http://www.tandfonline.com/doi/abs/10.1080/02664760601004940",
abstract = "Digits in statistical data produced by natural or
social processes are often distributed in a manner
described by `Benford's law'. Recently, a test against
this distribution was used to identify fraudulent
accounting data. This test is based on the supposition
that first, second, third, and other digits in real
data follow the Benford distribution while the digits
in fabricated data do not. Is it possible to apply
Benford tests to detect fabricated or falsified
scientific data as well as fraudulent financial data?
We approached this question in two ways. First, we
examined the use of the Benford distribution as a
standard by checking the frequencies of the nine
possible first and ten possible second digits in
published statistical estimates. Second, we conducted
experiments in which subjects were asked to fabricate
statistical estimates (regression coefficients). The
digits in these experimental data were scrutinized for
possible deviations from the Benford distribution.
There were two main findings. First, both digits of the
published regression coefficients were approximately
Benford distributed or at least followed a pattern of
monotonic decline. Second, the experimental results
yielded new insights into the strengths and weaknesses
of Benford tests. Surprisingly, first digits of faked
data also exhibited a pattern of monotonic decline,
while second, third, and fourth digits were distributed
less in accordance with Benford's law. At least in the
case of regression coefficients, there were indications
that checks for digit-preference anomalies should focus
less on the first (i.e., leftmost) and more on later
digits.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
keywords = "Benford's Law; data fabrication; digital analysis;
distribution of digits from regression coefficients;
first digit law; Zipf's Law",
}
@Article{Dumbgen:2007:EBA,
author = "L. D{\"u}mbgen and C. Leuenberger",
title = "Explicit bounds for the approximation error in
{Benford}'s law",
journal = "ArXiv e-prints",
month = may,
year = "2007",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2007arXiv0705.4488D",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0705.4488",
keywords = "Mathematics - Probability, 60E15, 60F99",
primaryclass = "math.PR",
}
@Article{Egghe:2007:UHL,
author = "Leo Egghe",
title = "Untangling {Herdan's Law} and {Heaps' Law}:
Mathematical and informetric arguments",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "58",
number = "5",
pages = "702--709",
year = "2007",
CODEN = "JASIEF",
DOI = "http://dx.doi.org/10.1002/asi.20524",
ISSN = "1532-2890",
ISSN-L = "1532-2882",
bibdate = "Mon Feb 25 08:31:49 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
keywords = "Heaps' law in information retrieval; Herdan's law in
linguistics",
}
@InProceedings{Fu:2007:GBL,
author = "D. Fu and Y. Q. Shi and W. Su",
editor = "Edward J. {Delp III} and Ping Wah Wong",
booktitle = "{Society of Photo-Optical Instrumentation Engineers
(SPIE)} Conference Series",
title = "A generalized {Benford}'s law for {JPEG} coefficients
and its applications in image forensics",
volume = "6505",
publisher = pub-SPIE,
address = pub-SPIE:adr,
month = feb,
year = "2007",
DOI = "http://dx.doi.org/10.1117/12.704723",
ISSN = "0277-786X (print), 1996-756X (electronic)",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Society of Photo-Optical Instrumentation Engineers
(SPIE) Conference Series",
URL = "http://adsabs.harvard.edu/abs/2007SPIE.6505E..55F",
acknowledgement = ack-nhfb,
}
@Article{Giles:2007:BLN,
author = "D. E. Giles",
title = "{Benford's Law} and naturally occurring prices in
certain {eBay} auctions",
journal = j-APPL-ECON-LETT,
volume = "14",
number = "3",
pages = "157--161",
year = "2007",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/13504850500425667",
ISSN = "1350-4851 (print), 1466-4291 (electronic)",
ISSN-L = "1350-4851",
bibdate = "Wed Nov 16 09:49:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/toc/rael20/current",
acknowledgement = ack-nhfb,
fjournal = "Applied Economics Letters",
keywords = "Benford's Law; Fibonacci sequences; Lucas sequences",
}
@Article{Grendar:2007:ENP,
author = "Marian Grendar and George Judge and Laura Schechter",
title = "An empirical non-parametric likelihood family of
data-based {Benford}-like distributions",
journal = j-PHYSICA-A,
volume = "380",
number = "0",
pages = "429--438",
day = "1",
month = jul,
year = "2007",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2007.02.062",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://adsabs.harvard.edu/abs/2007PhyA..380..429G;
http://www.sciencedirect.com/science/article/pii/S0378437107001963",
abstract = "A mathematical expression known as Benford's law
provides an example of an unexpected relationship among
randomly selected sequences of first significant digits
(FSDs). Newcomb [Note on the frequency of use of the
different digits in natural numbers, Am. J. Math. 4
(1881) 39 40], and later Benford [The law of anomalous
numbers, Proc. Am. Philos. Soc. 78(4) (1938) 551 572],
conjectured that {FSDs} would exhibit a weakly
monotonic decreasing distribution and proposed a
frequency proportional to the logarithmic rule.
Unfortunately, the Benford {FSD} function does not hold
for a wide range of scale-invariant multiplicative
data. To confront this problem we use
information-theoretic methods to develop a data-based
family of alternative Benford-like exponential
distributions that provide null hypotheses for testing
purposes. Two data sets are used to illustrate the
performance of generalized Benford-like
distributions.",
acknowledgement = ack-nhfb,
fjournal = "Physica A: Statistical Mechanics and its
Applications",
keywords = "Benford's Law; Empirical likelihood; First significant
digit phenomenon; Information-theoretic method;
Minimum-divergence distance measure; Relative
frequencies",
}
@Article{Guo:2007:DIM,
author = "Lei Guo and Enhua Tan and Songqing Chen and Zhen Xiao
and Xiaodong Zhang",
title = "Does {Internet} media traffic really follow
{Zipf}-like distribution?",
journal = j-SIGMETRICS,
volume = "35",
number = "1",
pages = "359--360",
month = jun,
year = "2007",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1254882.1254929",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Fri Jun 27 09:42:48 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "It is commonly agreed that Web traffic follows the
Zipf-like distribution, which is an analytical
foundation for improving Web access performance by
client-server based proxy caching systems on the
Internet. However, some recent studies have observed
non-Zipf-like distributions of Internet media traffic
in different content delivery systems. Due to the
variety of media delivery systems and the diversity of
media content, existing studies on media traffic are
largely workload specific, and the observed access
patterns are often different from or even conflict with
each other. For Web media systems, study [3] reports
that the access pattern of streaming media is Zipf-like
in a university campus network, while study [2] finds
that it is not Zipf-like in an enterprise media
server.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
journal-URL = "http://portal.acm.org/toc.cfm?id=J618",
keywords = "media; stretched exponential; Zipf-like",
}
@Article{Gupta:2007:IMS,
author = "Arjun K. Gupta and Saralees Nadarajah",
title = "Information matrices for some bivariate {Pareto}
distributions",
journal = j-APPL-MATH-COMP,
volume = "184",
number = "2",
pages = "1069--1079",
day = "15",
month = jan,
year = "2007",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:03:01 MDT 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/science/journal/00963003",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Hand:2007:DDD,
author = "David Hand",
title = "Deception and Dishonesty with Data: Fraud in Science",
journal = j-SIGNIF,
volume = "4",
number = "1",
pages = "22--25",
month = mar,
year = "2007",
CODEN = "????",
DOI = "http://dx.doi.org/10.1111/j.1740-9713.2007.00215.x",
ISSN = "1740-9705 (print), 1740-9713 (electronic)",
ISSN-L = "1740-9705",
bibdate = "Thu Nov 17 19:17:58 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Significance ({Oxford, England})",
}
@Article{Hasumi:2007:ITS,
author = "Tomohiro Hasumi",
title = "Interoccurrence time statistics in the two-dimensional
{Burridge--Knopoff} earthquake model",
journal = j-PHYS-REV-E,
volume = "76",
number = "??",
pages = "026117",
day = "29",
month = aug,
year = "2007",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.76.026117",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.76.026117",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf--Mandelbrot law",
}
@TechReport{Hungerbuhler:2007:BGF,
author = "Norbert H{\"u}ngerb{\"u}hler",
title = "{Benfords Gesetz {\"u}ber f{\"u}hrende Ziffern. Wie
die Mathematik Steuers{\"u}ndern das F{\"u}rchten
lehrt} [{Benford's Law} on leading digits. Mathematics
teaches tax evaders to fear]",
type = "Report",
institution = "EducETH",
address = "Z{\"u}rich, Switzerland",
pages = "24",
day = "2",
month = mar,
year = "2007",
bibdate = "Fri Nov 18 12:02:21 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.educ.ethz.ch/unt/um/mathe/ana/benford/Benford_Fuehrende_Ziffern.pdf",
acknowledgement = ack-nhfb,
language = "German",
lastaccess = "18 November 2011",
remark = "This report has several nice figures, including
photographs of Newcomb, Benford, and worn pages of log
tables, and an amazing plot of the agreement of
200,125,088 mathematical constants with Benford's
Law.",
}
@Article{Kumar:2007:DDD,
author = "Kuldeep Kumar and Sukanto Bhattacharya",
title = "Detecting the dubious digits: {Benford}'s law in
forensic accounting",
journal = j-SIGNIF,
volume = "4",
number = "2",
pages = "81--83",
month = jun,
year = "2007",
CODEN = "????",
DOI = "http://dx.doi.org/10.1111/j.1740-9713.2007.00234.x",
ISSN = "1740-9705 (print), 1740-9713 (electronic)",
ISSN-L = "1740-9705",
MRnumber = "2380610",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://onlinelibrary.wiley.com/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Significance ({Oxford, England})",
onlinedate = "7 Jun 2007",
}
@Article{Mansury:2007:EZL,
author = "Yuri Mansury and L{\'a}szl{\'o} Guly{\'a}s",
title = "The emergence of {Zipf's Law} in a system of cities:
an agent-based simulation approach",
journal = j-J-ECON-DYN-CONTROL,
volume = "31",
number = "7",
pages = "2438--2460",
day = "15",
month = jul,
year = "2007",
CODEN = "JEDCDH",
DOI = "http://dx.doi.org/10.1016/j.jedc.2006.08.002",
ISSN = "0165-1889 (print), 1879-1743 (electronic)",
ISSN-L = "0165-1889",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165188906001527",
ZMnumber = "1163.91504",
abstract = "This paper develops a spatial agent-based model to
generate a system of cities that exhibits the
statistical properties of the Zipf's Law. The numerical
results suggest that the combination of bounded
rationality and maximum heterogeneity of agents can
produce a generic power-law relationship in the size
distribution of cities, but does not always generate
the Zipf's Law. We found sufficient conditions on the
probability distribution of spatial reach to generate
the Zipf's Law associated with unit power coefficient.
Our model also indicates that the Zipf's Law breaks
down unless the extent of agglomeration economies
overwhelms the negative disagglomerating forces.",
acknowledgement = ack-nhfb,
classmath = "91B72 (Spatial models)",
fjournal = "Journal of Economic Dynamics and Control",
keywords = "complex systems; power laws; spatial agent based
models; Zipf's Law",
}
@Article{Maslov:2007:PTZ,
author = "V. P. Maslov",
title = "Phase transitions of the zeroth kind and the
quantization of the {Zipf} law",
journal = j-TEORET-MATH-FIZ,
volume = "150",
number = "1",
pages = "118--142",
year = "2007",
CODEN = "TMFZAL",
DOI = "http://dx.doi.org/10.1007/s11232-007-0008-1",
ISSN = "0564-6162",
ISSN-L = "0564-6162",
MRclass = "82B26 (82B03)",
MRnumber = "2325869 (2008g:82037)",
MRreviewer = "N. N. Ganikhodjaev",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
Matematicheskaya Fizika",
}
@InProceedings{Mebane:2007:SD,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{2007 Summer Meeting of the Political Methodology
Society, Pennsylvania State University, July 18--21,
2007}",
title = "Statistics for Digits",
publisher = "????",
address = "????",
pages = "1--21",
day = "2",
month = jul,
year = "2007",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 12:03:01 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.umich.edu/~wmebane/pm07.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Nadarajah:2007:CPG,
author = "Saralees Nadarajah and Samuel Kotz",
title = "On the convolution of {Pareto} and gamma
distributions",
journal = j-COMP-NET-AMSTERDAM,
volume = "51",
number = "12",
pages = "3650--3654",
day = "22",
month = aug,
year = "2007",
CODEN = "????",
ISSN = "1389-1286 (print), 1872-7069 (electronic)",
ISSN-L = "1389-1286",
bibdate = "Sat Apr 2 08:42:20 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/science/journal/13891286",
acknowledgement = ack-nhfb,
fjournal = "Computer Networks",
journal-URL = "http://www.sciencedirect.com/science/journal/13891286",
}
@Article{Nicolaisen:2007:PPB,
author = "Jeppe Nicolaisen and Birger Hj{\o}rland",
title = "Practical potentials of {Bradford}'s law: a critical
examination of the received view",
journal = j-J-DOC,
volume = "63",
number = "3",
pages = "359--377",
month = "????",
year = "2007",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/00220410710743298",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 11:58:03 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@Article{Nigrini:2007:BLA,
author = "Mark J. Nigrini and Steven J. Miller",
title = "{Benford's Law} Applied to Hydrology Data --- Results
and Relevance to Other Geophysical Data",
journal = j-MATH-GEOL,
volume = "39",
number = "5",
pages = "469--490",
month = jul,
year = "2007",
CODEN = "MATGED",
DOI = "http://dx.doi.org/10.1007/s11004-007-9109-5",
ISSN = "0882-8121 (print), 1573-8868 (electronic)",
ISSN-L = "0882-8121",
bibdate = "Sun Feb 17 13:35:42 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007%2Fs11004-007-9109-5;
http://www.springerlink.com/content/m2274ng70435u3x6/",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Geology",
}
@Article{Nye:2007:PEN,
author = "J. Nye and C. Moul",
title = "The Political Economy of Numbers: On the Application
of {Benford's Law} to International Macroeconomic
Statistics",
journal = "{B. E.} Journal of Macroeconomics",
volume = "7",
number = "1",
pages = "??--??",
month = "????",
year = "2007",
CODEN = "????",
DOI = "http://dx.doi.org/10.2202/1935-1690.1449",
ISSN = "1935-1690",
ISSN-L = "1935-1690",
bibdate = "Tue Nov 22 20:48:42 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.bepress.com/bejm/vol7/iss1/art17",
acknowledgement = ack-nhfb,
articleno = "17",
fjournal = "Berkeley Electronic Press Journal of Macroeconomics",
}
@Article{Oteo:2007:DPE,
author = "J. A. Oteo and J. Ros",
title = "Double precision errors in the logistic map:
Statistical study and dynamical interpretation",
journal = j-PHYS-REV-E,
volume = "76",
pages = "036214",
month = sep,
year = "2007",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.76.036214",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:35:43 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.76.036214",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
issue = "3",
journal-URL = "http://pre.aps.org/browse",
pagecount = "8",
remark = "From the abstract: ``a comparison with Benford?s law
for the distribution of the leading digit of
compilation of numbers is discussed.''",
}
@Article{Paech:2007:ZLN,
author = "Kerstin Paech and Wolfgang Bauer and Scott Pratt",
title = "{Zipf}'s law in nuclear multifragmentation and
percolation theory",
journal = j-PHYS-REV-C,
volume = "76",
number = "??",
pages = "054603",
day = "15",
month = nov,
year = "2007",
CODEN = "PRVCAN",
DOI = "http://dx.doi.org/10.1103/PhysRevC.76.054603",
ISSN = "0556-2813 (print), 1089-490X, 1538-4497",
ISSN-L = "0556-2813",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevC.76.054603",
acknowledgement = ack-nhfb,
fjournal = "Physical Review C (Nuclear Physics)",
journal-URL = "http://prc.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Simons:2007:SIP,
author = "John L. Simons",
title = "A simple (inductive) proof for the non-existence of
2-cycles of the $ 3 x + 1 $ problem",
journal = j-J-NUMBER-THEORY,
volume = "123",
number = "1",
pages = "10--17",
month = mar,
year = "2007",
CODEN = "JNUTA9",
DOI = "http://dx.doi.org/10.1016/j.jnt.2006.05.011",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X06001223",
acknowledgement = ack-nhfb,
fjournal = "Journal of Number Theory",
keywords = "Benford's Law",
}
@Book{Tijms:2007:UPC,
author = "H. C. Tijms",
title = "Understanding probability: chance rules in everyday
life",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Second",
pages = "x + 442",
year = "2007",
ISBN = "0-511-34626-3 (e-book), 0-511-35003-1 (e-book),
0-521-70172-4 (paperback)",
ISBN-13 = "978-0-511-34626-2 (e-book), 978-0-511-35003-0
(e-book), 978-0-521-70172-3 (paperback)",
LCCN = "QA273 .T48 2007",
bibdate = "Mon Feb 18 06:48:08 MST 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
subject = "Probabilities; Mathematical analysis; Chance;
Mathematics; Probability and Statistics; General;
Waarschijnlijkheidstheorie;
Wahrscheinlichkeitsverteilung",
tableofcontents = "Probability questions \\
The law of large numbers and simulation \\
Probabilities in everyday life \\
Rare events and lotteries \\
Probability and statistics \\
Chance trees and Bayes' rule \\
Foundations of probability theory \\
Conditional probability and Bayes \\
Basic rules for discrete random variables \\
Continuous random variables \\
Jointly distributed random variables \\
Multivariate normal distribution \\
Conditional distributions \\
Generating functions \\
Markov chains",
}
@Article{Torres:2007:HDN,
author = "J. Torres and S. Fern{\'a}ndez and A. Gamero and A.
Sola",
title = "How do numbers begin? (the first digit law)",
journal = j-EUR-J-PHYS,
volume = "28",
number = "3",
pages = "L17--L25",
month = may,
year = "2007",
CODEN = "EJPHD4",
DOI = "http://dx.doi.org/10.1088/0143-0807/28/3/N04",
ISSN = "0143-0807 (print), 1361-6404 (electronic)",
ISSN-L = "0143-0807",
bibdate = "Fri Feb 15 18:37:16 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://iopscience.iop.org/0143-0807/28/3/N04",
acknowledgement = ack-nhfb,
fjournal = "European Journal of Physics",
journal-URL = "http://iopscience.iop.org/0143-0807/",
keywords = "Benford's Law; Frank Benford; Simon Newcomb",
remark-1 = "From page L19: ``He [Newcomb] founded the American
Astronomical Society, and was its first president; he
was a successful scientist.''.",
remark-2 = "From page L19: ``His [Newcomb's] discovery went
unnoticed by the scientific community, in spite of the
fact that Newcomb was already a famous scientist at the
time. He continued working in physical and mathematical
astronomy, receiving honours for his career --- a
crater of Mars takes his name --- but he was also
responsible for a famous funny mistake: he tried to
demonstrate that an object heavier than air could not
fly, just months before the Wright brothers' first
one-man aeroplane flew in 1903. Far from retracting,
Newcomb said that an aeroplane for two or more people
could not fly, so aeroplanes would not be worthwhile
pursuing [3, 4]. He died in 1909, without even
remembering the matter of the first significant digit
law.'',",
remark-3 = "From page L19: ``Frank Benford, a physicist working at
General Electric (who was the inventor of the electric
light pointer), \ldots{}''.",
}
@Article{Wells:2007:QPV,
author = "K. Wells and J. Chiverton and M. Partridge and M.
Barry and H. Kadhem and B. Ott",
title = "Quantifying the Partial Volume Effect in {PET} Using
{Benford's Law}",
journal = j-IEEE-TRANS-NUCL-SCI,
volume = "54",
number = "5",
pages = "1616--1625",
month = oct,
year = "2007",
CODEN = "IRNSAM",
DOI = "http://dx.doi.org/10.1109/TNS.2007.903182",
ISSN = "0018-9499 (print), 1558-1578 (electronic)",
ISSN-L = "0018-9499",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2007ITNS...54.1616W",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Nuclear Science",
}
@Article{Yeh:2007:SMD,
author = "Hsiaw-Chan Yeh",
title = "Some multivariate discrete time series models for
dependent multivariate {Zipf} counts",
journal = "Bulletin of the Institute of Mathematics. Academia
Sinica. New Series",
volume = "2",
number = "1",
pages = "29--53",
year = "2007",
CODEN = "????",
ISSN = "0304-9825",
ISSN-L = "0304-9825",
MRclass = "62M10 (62H20)",
MRnumber = "2294107",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Bull. Inst. Math. Acad. Sin. (N.S.)",
fjournal = "Bulletin of the Institute of Mathematics. Academia
Sinica. New Series",
}
@Article{Aerts:2008:CDD,
author = "Walter Aerts and Geert {Van Campenhout} and Tom {Van
Caneghem}",
title = "Clustering in dividends: Do managers rely on cognitive
reference points?",
journal = "Journal of Economic Psychology",
volume = "29",
number = "3",
pages = "276--284",
year = "2008",
DOI = "http://dx.doi.org/10.1016/j.joep.2007.10.003",
ISSN = "0167-4870",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167487007000864",
abstract = "Prior studies (see e.g. [Rosch, E. (1975). Cognitive
reference points. Cognitive Psychology, {\bf 7},
532--547]) indicate that multiples of ten serve as
cognitive reference points with a view to perceiving
and evaluating numbers. In order to explore whether
managers set dividends per share (henceforth DPS) at or
just above a cognitive reference point, we perform a
digital analysis on {US} firms' {DPS} for the period
1995--2004. That is, based on the theory of cognitive
reference points, {DPS} of \$2.00 will be viewed as
being abnormally larger than {DPS} of \$1.99, whereas
the actual difference only amounts to a marginal
\$0.01. Results presented in this paper indicate that
managers fall back on cognitive reference points when
they set DPS, which shows in significantly more (fewer)
zeroes (large digits) in the second-from-the-left
position of {DPS} than would normally be expected.
Overall, results presented in this paper tally with
prior findings on odd-ending prices and price
clustering documented in related disciplines.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Cognitive psychology; Management",
}
@Article{Aono:2008:ISO,
author = "June Y. Aono and Liming Guan",
title = "The impact of {Sarbanes--Oxley} act on cosmetic
earnings management",
journal = "Research in Accounting Regulation",
volume = "20",
number = "0",
pages = "205--215",
month = oct,
year = "2008",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/S1052-0457(07)00212-3",
ISSN = "1052-0457",
ISSN-L = "1052-0457",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S1052045707002123",
abstract = "This study examines the mitigating effect of
Sarbanes--Oxley Act on cosmetic earnings management,
referred by Kinnunen and Koskela (2003) as earnings
manipulative behavior to round earnings such that they
result in an upward bias. This behavior reports income
numbers to achieve key cognitive reference points
represented by $ N \times $ 10k. Using Benford's Law,
our analysis compares the distribution of second digits
in reported annual net income for publicly listed {US}
companies between a 2-year periods before and after the
year 2002 when Sarbanes--Oxley Act went into effect.
Our empirical results suggest that, in the 2-year
period prior to the Act, there was evidence of cosmetic
earnings management. However, such behavior in
manipulating net income has noticeably decreased in the
period after the Act. This finding is consistent with
the notion that Sarbanes--Oxley Act has a deterring
impact on corporate America's manipulative behavior to
report earnings that achieve certain key reference
points.",
acknowledgement = ack-nhfb,
fjournal = "Research in Accounting Regulation",
keywords = "Benford's Law",
}
@Article{Batty:2008:PSS,
author = "Michael Batty",
title = "Perspective: The Size, Scale, and Shape of Cities",
journal = j-SCIENCE,
volume = "318",
number = "5864",
pages = "769--771",
day = "8",
month = feb,
year = "2008",
CODEN = "SCIEAS",
DOI = "http://dx.doi.org/10.1126/science.1151419",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Wed Feb 27 06:02:28 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencemag.org/content/319/5864/769.abstract",
acknowledgement = ack-nhfb,
fjournal = "Science",
journal-URL = "http://www.sciencemag.org/archive/",
keywords = "200 tallest buildings in world; US cities of one
million (or more) population; Zipf's law",
}
@Article{Bhattacharya:2008:FAB,
author = "S. Bhattacharya and K. Kumar",
title = "Forensic Accounting and {Benford's Law} [In the
Spotlight]",
journal = j-IEEE-SIGNAL-PROCESS-MAG,
volume = "25",
number = "2",
pages = "152--150",
month = mar,
year = "2008",
CODEN = "ISPRE6",
DOI = "http://dx.doi.org/10.1109/MSP.2007.914724",
ISSN = "1053-5888 (print), 1558-0792 (electronic)",
ISSN-L = "1053-5888",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008ISPM...25..152B",
acknowledgement = ack-nhfb,
fjournal = "IEEE signal processing magazine",
}
@Article{Brown:2008:CSP,
author = "Philip Brown and Jason Mitchell",
title = "Culture and stock price clustering: Evidence from {The
Peoples' Republic of China}",
journal = "Pacific-Basin Finance Journal",
volume = "16",
number = "1 2",
pages = "95--120",
year = "2008",
DOI = "http://dx.doi.org/10.1016/j.pacfin.2007.04.005",
ISSN = "0927-538X",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Behavioral Finance in Asia",
URL = "http://www.sciencedirect.com/science/article/pii/S0927538X0700025X",
abstract = "Price clustering is the tendency of prices to be
observed more frequently at some numbers than others.
It results from human bias and from haziness or
imprecise beliefs about underlying value. To many
Chinese, the number 8 is attractive because it is
considered lucky, while 4 is unlucky and to be avoided.
We conduct a tightly controlled experiment to determine
whether a culturally heuristic number preference
exists, by studying trading on the Shanghai and
Shenzhen stock exchanges, which historically have been
relatively segmented along cultural lines. Our results
are extremely clear. For much of our sample period
(1994 2002), the prices of A-shares (mostly held by
Chinese organisations or individuals) traded on the
Shanghai stock exchange were more than twice as likely
to end in 8, than 4. Similarly, for A-shares traded on
the Shenzhen stock exchange a preference for 8 was
found. Preference for 8 on both exchanges was initially
very strong, but has weakened somewhat over time. It is
observed in opening, high and low as well as closing
prices, reinforcing its pervasiveness. Overall, the
cultural preference manifest in the prices of A-shares
is widespread in both markets and its presence is
accentuated once other factors that influence price
clustering are taken into account. The preference for 8
was much weaker for B-shares, which largely have been
held by foreigners.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Feng shui; Number preferences; Shanghai
and Shenzhen stock exchanges; Stock price clustering",
}
@Article{Chakravorty:2008:TAE,
author = "Douglas N. Hales and V. Sridharan and Abirami
Radhakrishnan and Satya S. Chakravorty and Samia M.
Siha",
title = "Testing the accuracy of employee-reported data: An
inexpensive alternative approach to traditional
methods",
journal = j-EUR-J-OPER-RES,
volume = "189",
number = "3",
pages = "583--593",
day = "16",
month = sep,
year = "2008",
CODEN = "EJORDT",
DOI = "http://dx.doi.org/10.1016/j.ejor.2006.09.092",
ISSN = "0377-2217 (print), 1872-6860 (electronic)",
ISSN-L = "0377-2217",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0377221706011702",
acknowledgement = ack-nhfb,
fjournal = "European Journal of Operational Research",
keywords = "Benford's Law",
xxauthor = "S. Chakravorty and Samia M. Siha",
}
@Article{Costas:2008:NCC,
author = "Eduardo Costas and Victoria L{\'o}pez-Rodas and F.
Javier Toro and Antonio Flores-Moya",
title = "The number of cells in colonies of the cyanobacterium
{{\em Microcystis aeruginosa\/}} satisfies {Benford}'s
law",
journal = j-AQUAT-BOT,
volume = "89",
number = "3",
pages = "341--343",
month = oct,
year = "2008",
CODEN = "AQBODS",
DOI = "http://dx.doi.org/10.1016/j.aquabot.2008.03.011",
ISSN = "0304-3770 (print), 1879-1522 (electronic)",
ISSN-L = "0304-3770",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0304377008000533",
abstract = "Nowadays, numerous power- or scaling-laws are
encountered in many fields of biology: an example is
Benford's law. According to this law, the first
significant digit of any given series of numbers is
figure 1 more often than figure 2, which in turn
appears more often than 3, and so on. Here we show that
number of cells per colony in the cyanobacterium
Microcystis aeruginosa (F.T. K{\"u}tzing) F.T.
K{\"u}tzing, randomly isolated from different
reservoirs and lakes from Andalusia (S Spain), was very
variable (with figures differing up to five orders of
magnitude). However, the distribution of the number of
cells per colony satisfies Benford's law. This
situation could be much more general in colonial
cyanobacteria.",
acknowledgement = ack-nhfb,
fjournal = "Aquatic Botany",
keywords = "Benford's Law; Colony; Microcystis aeruginosa",
}
@Article{Depken:2008:BZB,
author = "Craig A. {Depken II}",
title = "{Benford}, {Zipf} and the blogosphere",
journal = j-APPL-ECON-LETT,
volume = "15",
number = "9",
pages = "689--692",
month = "????",
year = "2008",
DOI = "http://dx.doi.org/10.1080/13504850600735270",
ISSN = "1350-4851 (print), 1466-4291 (electronic)",
ISSN-L = "1350-4851",
bibdate = "Sat Jan 07 09:18:33 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/13504850600735270",
acknowledgement = ack-nhfb,
fjournal = "Applied Economics Letters",
onlinedate = "04 Jul 2008",
}
@Article{Dumbgen:2008:EBA,
author = "Lutz D{\"u}mbgen and Christoph Leuenberger",
title = "Explicit bounds for the approximation error in
{Benford}'s law",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "99--112",
year = "2008",
CODEN = "????",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60E15 (60F99)",
MRnumber = "2386066 (2009b:60056)",
MRreviewer = "Pieter C. Allaart",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://arxiv.org/abs/0705.4488;
http://weber.math.washington.edu/~ejpecp/ECP/index.php",
abstract = "Benford's law states that for many random variables $
X > 0 $ its leading digit $ D = D(X) $ satisfies
approximately the equation $ P(D = d) = \log_{10}(1 + 1
/ d) $ for $ d = 1, 2, \ldots {}, 9 $. This phenomenon
follows from another, maybe more intuitive fact,
applied to $ Y := \log_{10}(X) $: For many real random
variables $Y$, the remainder $ U := Y - \floor (Y) $ is
approximately uniformly distributed on $ [0, 1) $. The
present paper provides new explicit bounds for the
latter approximation in terms of the total variation of
the density of $Y$ or some derivative of it. These
bounds are an interesting alternative to traditional
Fourier methods which yield mostly qualitative results.
As a by-product we obtain explicit bounds for the
approximation error in Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Gauvrit:2008:PLB,
author = "Nicolas Gauvrit and Jean-Paul Delahaye",
title = "Pourquoi la loi de {Benford} n'est pas
myst{\'e}rieuse. ({French}) [{Why} {Benford}'s law is
not mysterious]",
journal = "Math{\'e}matiques et Sciences Humaines = Mathematics
and Social Sciences",
volume = "46",
number = "182",
pages = "7--15",
year = "2008",
CODEN = "????",
ISSN = "0987-6936 (print), 1950-6821 (electronic)",
ISSN-L = "0987-6936",
MRclass = "62A01 (91E10)",
MRnumber = "2433183 (2009f:62008)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.ehess.fr/revue-msh/pdf/N182R1280.pdf",
acknowledgement = ack-nhfb,
ajournal = "Math. Sci. Hum. Math. Soc. Sci.",
fjournal = "Math{\'e}matiques et Sciences Humaines= Mathematics
and Social Sciences",
language = "French",
}
@Article{Hales:2008:TAE,
author = "Douglas N. Hales and V. Sridharan and Abirami
Radhakrishnan and Satya S. Chakravorty and Samia M.
Siha",
title = "Testing the accuracy of employee-reported data: An
inexpensive alternative approach to traditional
methods",
journal = j-EUR-J-OPER-RES,
volume = "189",
number = "3",
pages = "583--593",
year = "2008",
CODEN = "EJORDT",
DOI = "http://dx.doi.org/10.1016/j.ejor.2006.09.092",
ISSN = "0377-2217",
ISSN-L = "0377-2217",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377221706011702",
abstract = "Although Information Technology (IT) solutions improve
the collection and validation of operational data,
Operations Managers must often rely on self-reported
data from workers to make decisions. The problem with
this data is that they are subject to intentional
manipulation, thus reducing their suitability for
decision-making. A method of identifying manipulated
data, digital analysis, addresses this problem at low
cost. In this paper, we demonstrate how one uses this
method in real-world companies to validate
self-reported data from line workers. The results of
our study suggest that digital analysis estimates the
accuracy of employee reported data in operations
management, within limited contexts. These findings
lead to improved operating performance by providing a
tool for practitioners to exclude inaccurate
information.",
acknowledgement = ack-nhfb,
fjournal = "European Journal of Operational Research",
keywords = "Benford's Law; Digital analysis; Fraud detection;
Operations management; Plastics industry",
}
@Article{Hefeeda:2008:TMP,
author = "Mohamed Hefeeda and Osama Saleh",
title = "Traffic modeling and proportional partial caching for
peer-to-peer systems",
journal = j-IEEE-TRANS-NETWORKING,
volume = "16",
number = "6",
pages = "1447--1460",
month = dec,
year = "2008",
CODEN = "IEANEP",
DOI = "http://dx.doi.org/10.1109/TNET.2008.918081",
ISSN = "1063-6692 (print), 1558-2566 (electronic)",
ISSN-L = "1063-6692",
bibdate = "Fri Mar 6 16:31:04 MST 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib",
abstract = "Peer-to-peer (P2P) file sharing systems generate a
major portion of the Internet traffic, and this portion
is expected to increase in the future. We explore the
potential of deploying proxy caches in different
Autonomous Systems (ASes) with the goal of reducing the
cost incurred by Internet service providers and
alleviating the load on the Internet backbone. We
conduct an eight-month measurement study to analyze the
P2P traffic characteristics that are relevant to
caching, such as object popularity, popularity
dynamics, and object size. Our study shows that the
popularity of P2P objects can be modeled by a
Mandelbrot-Zipf distribution, and that several
workloads exist in P2P traffic. Guided by our findings,
we develop a novel caching algorithm for P2P traffic
that is based on object segmentation, and proportional
partial admission and eviction of objects. Our
trace-based simulations show that with a relatively
small cache size, a byte hit rate of up to 35\% can be
achieved by our algorithm, which is close to the byte
hit rate achieved by an off-line optimal algorithm with
complete knowledge of future requests. Our results also
show that our algorithm achieves a byte hit rate that
is at least 40\% more, and at most triple, the byte hit
rate of the common web caching algorithms. Furthermore,
our algorithm is robust in face of aborted downloads,
which is a common case in P2P systems.",
acknowledgement = ack-nhfb,
fjournal = "IEEE\slash ACM Transactions on Networking",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J771",
keywords = "internet measurement; network protocols; peer-to-peer
systems; traffic analysis; traffic modeling",
}
@Article{Huang:2008:IZL,
author = "Shi-Ming Huang and David C. Yen and Luen-Wei Yang and
Jing-Shiuan Hua",
title = "An investigation of {Zipf's Law} for fraud detection
{(DSS\# 06-10-1826R(2))}",
journal = j-DEC-SUPP-SYS,
volume = "46",
number = "1",
pages = "70--83",
month = dec,
year = "2008",
CODEN = "DSSYDK",
DOI = "http://dx.doi.org/10.1016/j.dss.2008.05.003",
ISSN = "0167-9236 (print), 1873-5797 (electronic)",
ISSN-L = "0167-9236",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167923608001073",
abstract = "Fraud risk is higher than ever before. Unfortunately,
many auditors lack the expertise to deal with the
related risks. The objectives of this research are to
develop an innovative fraud detection mechanism on the
basis of Zipf's Law. The purpose of this technique is
to assist auditors in reviewing the overwhelming
volumes of datasets and identifying any potential fraud
records. The authors conducted Quasi-experiment
research on the KDDCUP'99 benchmark intrusion detection
dataset to verify the performance of the proposed
mechanism. The simulation experimental results
demonstrate that Zipf Analysis can assist auditors to
locate the source of suspicion and further enhance the
resulting audit processes.",
acknowledgement = ack-nhfb,
fjournal = "Decision Support Systems",
keywords = "Benford's Law; Fraud detection; Misclassification cost
matrix; Quasi-experiment research; Zipf's Law",
}
@Article{Humenberger:2008:EBB,
author = "H. Humenberger",
title = "{Eine elementarmathematische Begr{\"u}ndung des
Benford-Gesetzes}. ({German}) [{An} elementary
mathematical derivation of the {Benford Law}]",
journal = "Der Mathematikunterricht",
volume = "54",
number = "??",
pages = "24--34",
month = "????",
year = "2008",
CODEN = "????",
ISSN = "0025-5807",
ISSN-L = "0025-5807",
bibdate = "Fri Nov 18 11:59:44 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.oemg.ac.at/DK/Didaktikhefte/2008%2520Band%252041/VortragHumenberger.pdf",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Ipeirotis:2008:CAH,
author = "Panagiotis G. Ipeirotis and Luis Gravano",
title = "Classification-aware hidden-web text database
selection",
journal = j-TOIS,
volume = "26",
number = "2",
pages = "6:1--6:??",
month = mar,
year = "2008",
CODEN = "ATISET",
DOI = "http://doi.acm.org/10.1145/1344411.1344412",
ISSN = "1046-8188",
ISSN-L = "0734-2047",
bibdate = "Thu Jun 12 16:52:34 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/tois/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Many valuable text databases on the web have
noncrawlable contents that are ``hidden'' behind search
interfaces. Metasearchers are helpful tools for
searching over multiple such ``hidden-web'' text
databases at once through a unified query interface. An
important step in the metasearching process is database
selection, or determining which databases are the most
relevant for a given user query. The state-of-the-art
database selection techniques rely on statistical
summaries of the database contents, generally including
the database vocabulary and associated word
frequencies. Unfortunately, hidden-web text databases
typically do not export such summaries, so previous
research has developed algorithms for constructing
approximate content summaries from document samples
extracted from the databases via querying. We present a
novel ``focused-probing'' sampling algorithm that
detects the topics covered in a database and adaptively
extracts documents that are representative of the topic
coverage of the database. Our algorithm is the first to
construct content summaries that include the
frequencies of the words in the database.
Unfortunately, Zipf's law practically guarantees that
for any relatively large database, content summaries
built from moderately sized document samples will fail
to cover many low-frequency words; in turn, incomplete
content summaries might negatively affect the database
selection process, especially for short queries with
infrequent words. To enhance the sparse document
samples and improve the database selection decisions,
we exploit the fact that topically similar databases
tend to have similar vocabularies, so samples extracted
from databases with a similar topical focus can
complement each other. We have developed two database
selection algorithms that exploit this observation. The
first algorithm proceeds hierarchically and selects the
best categories for a query, and then sends the query
to the appropriate databases in the chosen categories.
The second algorithm uses ``shrinkage,'' a statistical
technique for improving parameter estimation in the
face of sparse data, to enhance the database content
summaries with category-specific words. We describe how
to modify existing database selection algorithms to
adaptively decide (at runtime) whether shrinkage is
beneficial for a query. A thorough evaluation over a
variety of databases, including 315 real web databases
as well as TREC data, suggests that the proposed
sampling methods generate high-quality content
summaries and that the database selection algorithms
produce significantly more relevant database selection
decisions and overall search results than existing
algorithms.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Information Systems (TOIS)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J779",
keywords = "database selection; Distributed information retrieval;
web search",
}
@Article{Jager:2008:DAD,
author = "Hendrik Jager and Pierre Liardet",
title = "Distributions arithm{\'e}tiques des d{\'e}nominateurs
de convergents de fractions continues. ({French})
[Arithmetic distributions of the denominators of
continued fractions]",
journal = "Proceedings of the Koninklijke Nederlandse Akademie
van Wetenschappen, Series A, Indagationes
mathematicae",
volume = "91",
number = "2",
pages = "181--197",
day = "20",
month = jun,
year = "2008",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/S1385-7258(88)80026-X",
ISSN = "1385-7258 (print), 1878-5972 (electronic)",
ISSN-L = "1385-7258",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S138572588880026X",
acknowledgement = ack-nhfb,
fjournal = "Indagationes Mathematicae (Proceedings)",
keywords = "Benford's Law",
language = "French",
xxjournal = "Indagationes Mathematicae (Proceedings)",
}
@Article{Jang:2008:CDH,
author = "D. Jang and J. U. Kang and A. Kruckman and J. Kudo and
S. J. Miller",
title = "Chains of distributions, hierarchical {Bayesian}
models and {Benford's Law}",
journal = "ArXiv e-prints",
month = may,
year = "2008",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J;
http://arxiv.org/abs/0805.4226",
abstract = "Kossovsky recently conjectured that the distribution
of leading digits of a chain of probability
distributions converges to Benford's law as the length
of the chain grows. We prove his conjecture in many
cases, and provide an interpretation in terms of
products of independent random variables and a central
limit theorem. An interesting consequence is that in
hierarchical Bayesian models priors tend to satisfy
Benford's Law as the number of levels of the hierarchy
increases, which allows us to develop some simple tests
(based on Benford's law) to test proposed models. We
give explicit formulas for the error terms as sums of
Mellin transforms, which converges extremely rapidly as
the number of terms in the chain grows. We may
interpret our results as showing that certain Markov
chain Monte Carlo processes are rapidly mixing to
Benford's law.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0805.4226",
keywords = "Mathematics - Probability, Mathematics - Statistics
Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)",
pagecount = "15",
primaryclass = "math.PR",
}
@Article{Jelenkovic:2008:CMS,
author = "Predrag R. Jelenkovi{\'c} and Xiaozhu Kang",
title = "Characterizing the miss sequence of the {LRU} cache",
journal = j-SIGMETRICS,
volume = "36",
number = "2",
pages = "119--121",
month = sep,
year = "2008",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1453175.1453203",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Wed Aug 25 07:31:09 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "Renewed interest in caching systems stems from their
wide-spread use for reducing the document download
latency over the Internet. Since caches are usually
organized in a hierarchical manner, it is important to
study the performance properties of tandem caches. The
first step in understanding this problem is to
characterize the miss stream from one single cache
since it represents the input to the next level cache.
In this regard, we discover that the miss stream from
one single cache is approximated well by the
superposition of a number of asymptotically independent
renewal processes. Interestingly, when this weakly
correlated miss sequence is fed into another cache,
this barely observable correlation can lead to
measurably different caching performance when compared
to the independent reference model. This result is
likely to enable the development of a rigorous analysis
of the tandem cache performance.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
journal-URL = "http://portal.acm.org/toc.cfm?id=J618",
keywords = "average-case analysis; cache fault probability;
hierarchical caching; least-recently-used caching; web
caching; Zipf's law",
}
@Article{Kafri:2008:SIS,
author = "Oded Kafri",
title = "Sociological Inequality and the {Second Law}",
journal = "ArXiv e-prints",
year = "2008",
bibdate = "Mon Nov 21 06:41:29 2011",
bibsource = "http://dblp.uni-trier.de;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/0805.3206",
abstract = "There are two fair ways to distribute particles in
boxes. The first way is to divide the particles equally
between the boxes. The second way, which is calculated
here, is to score fairly the particles between the
boxes. The obtained power law distribution function
yields an uneven distribution of particles in boxes. It
is shown that the obtained distribution fits well to
sociological phenomena, such as the distribution of
votes in polls and the distribution of wealth and
Benford's law.",
acknowledgement = ack-nhfb,
}
@InProceedings{Krakar:2008:ABL,
author = "Zdravko Krakar and Mario {\v{Z}}gela",
editor = "Boris Aurer and Miroslav Ba{\'c}a",
booktitle = "Proceedings of the 19th Central European Conference on
Information and Intelligent Systems (CECIS 2008)",
title = "Application of {Benford's Law} in Payment System
Auditing",
publisher = "Fakultet organizacije i informatike",
address = "Vara{\v{z}}din, Croatia",
pages = "187--193",
year = "2008",
bibdate = "Sun Nov 13 11:14:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Krakar:2008:EBL,
author = "Zdravko Krakar and Mario {\v{Z}}gela",
editor = "Mario Plenkovi{\'c}",
booktitle = "Society and Technology 2008",
title = "Evaluation of {Benford's Law}: application in stock
prices and stock turnover",
publisher = "Hrvatsko komunikolo{\v{s}}ko dru{\v{s}}tvo",
address = "Zagreb, Croatia",
pages = "57--71",
year = "2008",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sun Nov 13 11:18:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
remark = "International Federation of Communication Studies,
Grafi{\v{c}}ki fakultet Sveu{\v{c}}ili{\v{s}}ta u
Zagrebu.",
}
@Article{Liu:2008:MNS,
author = "Cheng-Shi Liu",
title = "Maximal non-symmetric entropy leads naturally to
{Zipf}'s law",
journal = j-FRACTALS,
volume = "16",
number = "1",
pages = "99--101",
year = "2008",
CODEN = "FRACEG",
DOI = "http://dx.doi.org/10.1142/S0218348X08003788",
ISSN = "0218-348X",
ISSN-L = "0218-348X",
MRclass = "94A17 (94A15)",
MRnumber = "2399875 (2009c:94027)",
MRreviewer = "Yasuichi Horibe",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Fractals. Complex Geometry, Patterns, and Scaling in
Nature and Society",
}
@Article{Lolbert:2008:NEG,
author = "Tam{\'a}s Lolbert",
title = "On the non-existence of a general {Benford}'s law",
journal = "Mathematical Social Sciences",
volume = "55",
number = "2",
pages = "103--106",
month = mar,
year = "2008",
CODEN = "MSOSDD",
DOI = "http://dx.doi.org/10.1016/j.mathsocsci.2007.09.001",
ISSN = "0165-4896 (print), 1879-3118 (electronic)",
ISSN-L = "0165-4896",
MRclass = "60A10 (60E10)",
MRnumber = "2391902",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165489607000935",
abstract = "Benford's law states that in randomly collected
numbers certain digits are more often leading digits
than others. More formally: the general law states that
the mantissae follow the logarithmic distribution in
any base. Benford's law was recognized by many
mathematicians so that several possible explanations
have been derived, but several questions are still
open. Applications are widespread, for example an
auditing technique (the so-called digital analysis),
which is employed around the world by internal revenue
services to detect tax fraud, is based on this
phenomenon.\par
In this paper it will be shown that there exists no
probability measure that would obey Benford's law for
any base, but if the set of possible bases does not
exceed a given upper limit, most real-life
distributions obey, or can be transformed to obey
Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Social Sciences",
keywords = "Benford's Law; Characteristic function; Mantissa;
Numeral base",
}
@Article{Luque:2008:FDF,
author = "Bartolo Luque and Lucas Lacasa",
title = "The first digit frequencies of primes and {Riemann}
zeta zeros tend to uniformity following a
size-dependent generalized {Benford}'s law",
journal = "ArXiv e-prints",
month = nov,
year = "2008",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See published paper \cite {Luque:2009:FDF}.",
URL = "http://adsabs.harvard.edu/abs/2008arXiv0811.3302L;
http://arxiv.org/abs/0811.3302",
abstract = "Prime numbers seem to distribute among the natural
numbers with no other law than that of chance, however
its global distribution presents a quite remarkable
smoothness. Such interplay between randomness and
regularity has motivated scientists of all ages to
search for local and global patterns in this
distribution that eventually could shed light into the
ultimate nature of primes. In this work we show that a
generalization of the well known first-digit Benford's
law, which addresses the rate of appearance of a given
leading digit $d$ in data sets, describes with
astonishing precision the statistical distribution of
leading digits in the prime numbers sequence. Moreover,
a reciprocal version of this pattern also takes place
in the sequence of the nontrivial Riemann zeta zeros.
We prove that the prime number theorem is, in the last
analysis, the responsible of these patterns. Some new
relations concerning the prime numbers distribution are
also deduced, including a new approximation to the
counting function $ \pi (n) $. Furthermore, some
relations concerning the statistical conformance to
this generalized Benford's law are derived. Some
applications are finally discussed.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0811.3302",
keywords = "Mathematics - Number Theory, Mathematics -
Probability, Mathematics - Statistics",
pagecount = "20",
primaryclass = "math.NT",
}
@Article{Maillart:2008:ETZ,
author = "T. Maillart and D. Sornette and S. Spaeth and G. von
Krogh",
title = "Empirical Tests of {Zipf's Law} Mechanism in Open
Source {Linux} Distribution",
journal = j-PHYS-REV-LET,
volume = "101",
number = "21",
pages = "218701",
day = "19",
month = nov,
year = "2008",
CODEN = "PRLTAO",
DOI = "http://dx.doi.org/10.1103/PhysRevLett.101.218701",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/gnu.bib;
http://www.math.utah.edu/pub/tex/bib/linux.bib;
http://www.math.utah.edu/pub/tex/bib/unix.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.101.218701",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
pagecount = "4",
}
@Article{Manin:2008:ZLA,
author = "Dmitrii Y. Manin",
title = "{Zipf's Law} and Avoidance of Excessive Synonymy",
journal = j-COGN-SCI,
volume = "32",
number = "7",
pages = "1075--1098",
year = "2008",
CODEN = "COGSD5",
DOI = "http://dx.doi.org/10.1080/03640210802020003",
ISSN = "0364-0213 (print), 1551-6709 (electronic)",
ISSN-L = "0364-0213",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Cognitive Science",
keywords = "Semantics; Synonymy; Word frequency; Word meaning;
Zipf's law",
}
@InProceedings{Mebane:2008:EFO,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{The American Electoral Process conference, Center for
the Study of Democratic Politics, Princeton University,
May 1--3, 2008}",
title = "Election Forensics: Outlier and Digit Tests in
{America} and {Russia}",
publisher = "????",
address = "????",
pages = "i + 26",
year = "2008",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 12:08:23 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.umich.edu/~wmebane/aep2008.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Mebane:2008:EFS,
author = "Walter R. {Mebane, Jr.}",
editor = "R. Michael Alvarez and Thad E. Hall and Susan D.
Hyde",
booktitle = "{The Art and Science of Studying Election Fraud:
Detection, Prevention, and Consequences}",
title = "Election Forensics: The Second-digit {Benford's Law}
Test and Recent {American Presidential} Elections",
publisher = "Brookings Institution",
address = "Washington, DC, USA",
pages = "ii + 30",
year = "2008",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 12:04:22 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Preprint dated 3 November 2006.",
URL = "http://www.umich.edu/~wmebane/fraud06.pdf",
acknowledgement = ack-nhfb,
remark = "An earlier version of this paper was presented at the
Election Fraud Conference, Salt Lake City, Utah,
September 29--30, 2006.",
}
@Article{Miller:2008:MCL,
author = "Steven J. Miller and Mark J. Nigrini",
title = "The modulo $1$ central limit theorem and {Benford}'s
law for products",
journal = "International Journal of Algebra",
volume = "2",
number = "1--4",
pages = "119--130",
year = "2008",
CODEN = "????",
ISSN = "1312-8868",
ISSN-L = "1312-8868",
MRclass = "60F05 (11K06 42A10)",
MRnumber = "2417189 (2009e:60053)",
MRreviewer = "Gutti J. Babu",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Algebra",
fjournal = "International Journal of Algebra",
}
@Article{Miller:2008:OSB,
author = "Steven J. Miller and Mark J. Nigrini",
title = "Order statistics and {Benford}'s law",
journal = j-INT-J-MATH-MATH-SCI,
year = "2008",
CODEN = "????",
ISSN = "0161-1712",
ISSN-L = "0161-1712",
MRclass = "62G30 (62E10)",
MRnumber = "2461421 (2010c:62168)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Article ID 382948.",
URL = "http://arxiv.org/abs/math/0601344",
abstract = "Fix a base $B$ and let zeta have the standard
exponential distribution; the distribution of digits of
zeta base $B$ is known to be very close to Benford's
Law. If there exists a $C$ such that the distribution
of digits of $C$ times the elements of some set is the
same as that of zeta, we say that set exhibits shifted
exponential behavior base $B$ (with a shift of $ \log_B
C \bmod 1 $ ). Let $ X_1, \ldots {}, X_N $ be
independent identically distributed random variables.
If the $ X_i $'s are drawn from the uniform
distribution on $ [0, L] $, then as $ N \to \infty $
the distribution of the digits of the differences
between adjacent order statistics converges to shifted
exponential behavior (with a shift of $ \log_B L / N
\bmod 1 $ ). By differentiating the cumulative
distribution function of the logarithms modulo 1,
applying Poisson Summation and then integrating the
resulting expression, we derive rapidly converging
explicit formulas measuring the deviations from
Benford's Law. Fix a delta in $ (0, 1) $ and choose $N$
independent random variables from any compactly
supported distribution with uniformly bounded first and
second derivatives and a second order Taylor series
expansion at each point. The distribution of digits of
any $ N^\delta $ consecutive differences {\em and\/}
all $ N - 1 $ normalized differences of the order
statistics exhibit shifted exponential behavior. We
derive conditions on the probability density which
determine whether or not the distribution of the digits
of all the un-normalized differences converges to
Benford's Law, shifted exponential behavior, or
oscillates between the two, and show that the Pareto
distribution leads to oscillating behavior.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematics and Mathematical
Sciences",
pagecount = "19",
}
@Article{Mitchell:2008:TST,
author = "James G. Mitchell and Laurent Seuront",
title = "Towards a seascape topology {II}: {Zipf} analysis of
one-dimensional patterns",
journal = j-J-MAR-SYST,
volume = "69",
number = "3--4",
pages = "328--338",
month = feb,
year = "2008",
CODEN = "JMASE5",
DOI = "http://dx.doi.org/10.1016/j.jmarsys.2006.03.026",
ISSN = "0924-7963 (print), 1879-1573 (electronic)",
ISSN-L = "0924-7963",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0924796307000632",
acknowledgement = ack-nhfb,
fjournal = "Journal of Marine Systems",
keywords = "Zipf's Law",
}
@Article{Mizuno:2008:PLE,
author = "Takayuki Mizuno and Masahiro Toriyama and Takao Terano
and Misako Takayasu",
title = "{Pareto} law of the expenditure of a person in
convenience stores",
journal = j-PHYSICA-A,
volume = "387",
number = "15",
pages = "3931--3935",
year = "2008",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2008.01.059",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "91B82",
MRnumber = "2586890",
bibdate = "Mon Feb 18 17:05:26 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
}
@Article{Ni:2008:BLH,
author = "D. Ni and Z. Ren",
title = "{Benford}'s law and half-lives of unstable nuclei",
journal = j-EUR-PHYS-J-A,
volume = "38",
pages = "251--255",
month = dec,
year = "2008",
CODEN = "EPJAFV",
DOI = "http://dx.doi.org/10.1140/epja/i2008-10680-8",
ISSN = "1434-6001 (print), 1434-601X (electronic)",
ISSN-L = "1434-6001",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008EPJA...38..251N",
acknowledgement = ack-nhfb,
fjournal = "European Physical Journal A: Hadrons and Nuclei",
journal-URL = "http://www.springerlink.com/content/1434-6001",
}
@Article{Pain:2008:BLC,
author = "Jean-Christophe Pain",
title = "{Benford}'s law and complex atomic spectra",
journal = j-PHYS-REV-E,
volume = "77",
number = "1",
pages = "012102",
month = jan,
year = "2008",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.77.012102",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008PhRvE..77a2102P;
http://pre.aps.org/abstract/PRE/v77/i1/e012102",
abstract = "We found that in transition arrays of complex atomic
spectra, the strengths of electric-dipolar lines obey
Benford's law, which means that their significant
digits follow a logarithmic distribution favoring the
smallest values. This indicates that atomic processes
result from the superposition of uncorrelated
probability laws and that the occurrence of digits
reflects the constraints induced by the selection
rules. Furthermore, Benford's law can be a useful test
of theoretical spectroscopic models. Its applicability
to the statistics of electric-dipolar lines can be
understood in the framework of random matrix theory and
is consistent with the Porter-Thomas law.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eid = "012102",
eprint = "0801.0946",
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Probability theory, Oscillator strengths, lifetimes,
transition moments, Other topics in the theory of the
electronic structure of atoms and molecules",
pagecount = "3",
primaryclass = "quant-ph",
}
@Article{Ravikumar:2008:BND,
author = "Bala Ravikumar",
title = "The {Benford--Newcomb} Distribution and Unambiguous
Context-Free Languages",
journal = j-INT-J-FOUND-COMP-SCI,
volume = "19",
number = "3",
pages = "717--727",
month = jun,
year = "2008",
CODEN = "IFCSEN",
DOI = "http://dx.doi.org/10.1142/S0129054108005905",
ISSN = "0129-0541 (print), 1793-6373 (electronic)",
ISSN-L = "0129-0541",
MRclass = "68Q42 (68Q25 68Q45)",
MRnumber = "2417964 (2009h:68068)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://ejournals.wspc.com.sg/ijfcs/mkt/archive.shtml;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Foundations of Computer
Science (IJFCS)",
journal-URL = "http://www.worldscientific.com/loi/ijfcs",
}
@Article{Schurger:2008:EBS,
author = "Klaus Sch{\"u}rger",
title = "Extensions of {Black--Scholes} processes and
{Benford's Law}",
journal = j-STOCH-PROC-APPL,
volume = "118",
number = "7",
pages = "1219--1243",
month = jul,
year = "2008",
CODEN = "STOPB7",
DOI = "http://dx.doi.org/10.1016/j.spa.2007.07.017",
ISSN = "0304-4149 (print), 1879-209X (electronic)",
ISSN-L = "0304-4149",
MRclass = "60F10 (60G44 91B02 91B28)",
MRnumber = "2428715 (2009g:60037)",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0304414907001391",
abstract = "Let $Z$ be a stochastic process of the form $ Z (t) =
Z (0) \exp (\mu t + X (t) - \langle X \rangle_t / 2) $
where $ Z (0) > 0 $, $ \mu $ are constants, and $X$ is
a continuous local martingale having a deterministic
quadratic variation $ \langle X \rangle $ such that $
\langle X \rangle_t \to \infty $ as $ t \to \infty $.
We show that the mantissa (base $b$) of $ Z (t)$
(denoted by $ M (b) (Z (t))$) converges weakly to
Benford's Law as $ t \to \infty $. Supposing that $X$
satisfies a certain growth condition, we obtain large
deviation results for certain functionals (including
occupation time) of ($ M^{(b)} (Z(t))$). Similar
results are obtained in the discrete-time case. The
latter are used to construct a non-parametric test for
nonnegative processes ( $ Z (t)$ ) (based on the
observation of significant digits of ( $ Z (n)$ ) ) of
the null hypothesis $ H_0 (\sigma_0)$ which says that
$Z$ is a general Black--Scholes process having a
volatility $ \sigma \geq \sigma_0 ( > 0)$. Finally it
is shown that the mantissa of Brownian motion is not
even weakly convergent.",
acknowledgement = ack-nhfb,
fjournal = "Stochastic Processes and Their Applications",
keywords = "Azuma's inequality; Benford's Law; Black Scholes
processes; Brownian motion; Exponential local
martingales; Large deviations; Leading digits;
Non-parametric hypothesis testing for processes;
Occupation time; Poisson's summation formula;
Significant digits; Strong theorems; Weak theorems",
}
@Article{Semboloni:2008:HCS,
author = "F. Semboloni",
title = "Hierarchy, cities size distribution and {Zipf}'s law",
journal = j-EUR-PHYS-J-B,
volume = "63",
number = "3",
pages = "295--301",
year = "2008",
CODEN = "EPJBFY",
DOI = "http://dx.doi.org/10.1140/epjb/e2008-00203-1",
ISSN = "1434-6028 (print), 1434-6036 (electronic)",
ISSN-L = "1434-6028",
MRclass = "91D10 (82B99 91D25)",
MRnumber = "2421552 (2009f:91111)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "Zbl 1189.91174",
acknowledgement = ack-nhfb,
fjournal = "The European Physical Journal B. Condensed Matter and
Complex Systems",
journal-URL = "http://link.springer.com/journal/10051",
}
@Article{Seuront:2008:TST,
author = "Laurent Seuront and James G. Mitchell",
title = "Towards a seascape typology. {I}. {Zipf} versus
{Pareto} laws",
journal = j-J-MAR-SYST,
volume = "69",
number = "3--4",
pages = "310--327",
month = feb,
year = "2008",
CODEN = "JMASE5",
DOI = "http://dx.doi.org/10.1016/j.jmarsys.2006.03.025",
ISSN = "0924-7963 (print), 1879-1573 (electronic)",
ISSN-L = "0924-7963",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0924796307000620",
acknowledgement = ack-nhfb,
fjournal = "Journal of Marine Systems",
keywords = "Zipf's Law",
}
@Article{Shaki:2008:RSN,
author = "Samuel Shaki and Martin H. Fischer",
title = "Reading space into numbers --- a cross-linguistic
comparison of the {SNARC} effect",
journal = j-COGNITION,
volume = "108",
number = "2",
pages = "590--599",
month = aug,
year = "2008",
CODEN = "CGTNAU",
DOI = "http://dx.doi.org/10.1016/j.cognition.2008.04.001",
ISSN = "0010-0277 (print), 1873-7838 (electronic)",
ISSN-L = "0010-0277",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0010027708000978",
abstract = "Small numbers are spontaneously associated with left
space and larger numbers with right space (the {SNARC}
effect), for example when classifying numbers by
parity. This effect is often attributed to reading
habits but a causal link has so far never been
documented. We report that bilingual Russian Hebrew
readers show a {SNARC} effect after reading Cyrillic
script (from left-to-right) that is significantly
reduced after reading Hebrew script (from
right-to-left). In contrast, they have similar {SNARC}
effects after listening to texts in either language.
These results support the view that spatially
directional scanning habits contribute to the spatial
association of numbers but also emphasize its
flexibility.",
acknowledgement = ack-nhfb,
fjournal = "Cognition",
keywords = "Benford's Law; Mental number line; Reading direction;
Spatial Numerical Association of Response Codes
(SNARC); {SNARC}",
}
@Article{Volchenkov:2008:SUC,
author = "D. Volchenkov and Ph. Blanchard",
title = "Scaling and universality in city space syntax: Between
{Zipf} and {Matthew}",
journal = j-PHYSICA-A,
volume = "387",
number = "10",
pages = "2353--2364",
day = "1",
month = apr,
year = "2008",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2007.11.049",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437107012630",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Article{Vuko:2008:UBL,
author = "Tina Vuko",
title = "Using {Benford's Law} to Detect Earnings Management
Practice: the Case of Listed Companies in {Croatia}",
journal = "Global Business \& Economics Anthology",
volume = "1",
number = "??",
pages = "69--74",
month = "????",
year = "2008",
CODEN = "????",
ISSN = "1553-1333",
ISSN-L = "1553-1333",
bibdate = "Sun Nov 13 11:10:55 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Watrin:2008:BLI,
author = "C. Watrin and R. Struffert and R. Ullmann",
title = "{Benford's Law}: An Instrument for Selecting Tax Audit
Targets?",
journal = "Review of Managerial Science",
volume = "2",
number = "3",
pages = "219--237",
month = nov,
year = "2008",
CODEN = "????",
DOI = "http://dx.doi.org/10.1007/s11846-008-0019-9",
ISSN = "1863-6683 (print), 1863-6691 (electronic)",
ISSN-L = "1863-6683",
bibdate = "Tue Nov 22 20:58:51 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Book{Ziliak:2008:CSS,
author = "Stephen Thomas Ziliak and Deirdre N. McCloskey",
title = "The Cult of Statistical Significance: How the Standard
Error Costs Us Jobs, Justice, and Lives",
publisher = "University of Michigan Press",
address = "Ann Arbor, MI, USA",
pages = "xxiii + 321",
year = "2008",
ISBN = "0-472-07007-X (cloth), 0-472-05007-9 (paperback)",
ISBN-13 = "978-0-472-07007-7 (cloth), 978-0-472-05007-9
(paperback)",
LCCN = "HB137 .Z55 2008",
bibdate = "Tue Dec 9 15:55:11 MST 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
series = "Economics, cognition, and society",
URL = "http://www.loc.gov/catdir/enhancements/fy0809/2007035401-d.html",
acknowledgement = ack-nhfb,
remark = "This book has important comments on the battles among
Sir Ronald Fisher, Jerzy Neyman, Egon Pearson, and Karl
Pearson, supplementing the discussion of those
conflicts in \cite{McGrayne:2011:TWH}.",
subject = "economics; statistical methods; statistics; social
aspects; statistical hypothesis testing",
}
@Article{Ainsworth:2009:QSR,
author = "Richard Thompson Ainsworth and Urs Hengartner",
title = "{Quebec's Sales Recording Module (SRM)}: Fighting the
{Zapper}, {Phantomware}, and Tax Fraud with
technology",
journal = "Canadian Tax Journal",
volume = "57",
number = "4",
pages = "715--761",
month = "????",
year = "2009",
CODEN = "????",
ISSN = "0068-9823",
ISSN-L = "0068-9823",
bibdate = "Fri Mar 22 08:37:54 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://www.ctf.ca/ctfweb/Documents/PDF/2009ctj/09ctj4-ainsworth.pdf",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
journal-URL = "https://www.ctf.ca/ctfweb",
keywords = "Benford's Law",
}
@TechReport{Alexander:2009:RUB,
author = "James C. Alexander",
title = "Remarks on the use of {Benford's Law}",
type = "Working paper",
institution = "Department of Mathematics and Cognitive Science, Case
Western Reserve University",
address = "Cleveland, OH, USA",
day = "23",
month = nov,
year = "2009",
bibdate = "Fri Mar 22 08:40:20 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1505147",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
}
@InProceedings{Altamirano:2009:GTU,
author = "Carlo Altamirano and Alberto Robledo",
editor = "J. Zhou",
booktitle = "Complex Sciences",
title = "Generalized Thermodynamics Underlying the Laws of
{Zipf} and {Benford}",
volume = "5",
publisher = pub-SV,
address = pub-SV:adr,
pages = "2232--??",
year = "2009",
DOI = "http://dx.doi.org/10.1007/978-3-642-02469-6_100",
ISBN = "3-642-02468-8",
ISBN-13 = "978-3-642-02468-9",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009cosc.conf.2232A",
acknowledgement = ack-nhfb,
}
@Article{Anderson:2009:CRC,
author = "Thomas Anderson",
title = "Conference reviewing considered harmful",
journal = j-OPER-SYS-REV,
volume = "43",
number = "2",
pages = "108--116",
month = apr,
year = "2009",
CODEN = "OSRED8",
DOI = "http://doi.acm.org/10.1145/1531793.1531815",
ISSN = "0163-5980 (print), 1943-586X (electronic)",
ISSN-L = "0163-5980",
bibdate = "Thu Apr 23 19:43:22 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "This paper develops a model of computer systems
research to help prospective authors understand the
often obscure workings of conference program
committees. We present data to show that the
variability between reviewers is often the dominant
factor as to whether a paper is accepted. We argue that
paper merit is likely to be Zipf distributed, making it
inherently difficult for program committees to
distinguish between most papers. We use game theory to
show that with noisy reviews and Zipf merit, authors
have an incentive to submit papers too early and too
often. These factors make conference reviewing, and
systems research as a whole, less efficient and less
effective. We describe some recent changes in
conference design to address these issues, and we
suggest some further potential improvements.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGOPS Operating Systems Review",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J597",
}
@Article{Battersby:2009:SAH,
author = "Stephen Battersby",
title = "Statistical analyses hint at fraud in {Iranian}
election",
journal = j-NEW-SCIENTIST,
volume = "202",
number = "2714",
pages = "10--??",
day = "24",
month = jun,
year = "2009",
CODEN = "NWSCAL",
DOI = "http://dx.doi.org/10.1016/S0262-4079(09)61682-1",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0262407909616821",
abstract = "Mathematicians add their own concerns to claims that
vote may have been rigged",
acknowledgement = ack-nhfb,
fjournal = "The New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
keywords = "Benford's Law",
xxISSN = "0262-4079, 0028-6664",
}
@TechReport{Bauer:2009:DDF,
author = "J. Bauer and J. Gross",
title = "Difficulties Detecting Fraud? {The} Use of {Benford's
Law} on Regression Tables",
type = "Report",
number = "??",
institution = "Institute of Sociology, LMU Munich",
address = "Munich, Germany",
month = "????",
year = "2009",
bibdate = "Fri Nov 18 11:46:08 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Berger:2009:BOB,
author = "A. Berger and T. P. Hill",
title = "{Benford} Online Bibliography",
institution = "Department of Mathematical and Statistical Sciences,
University of Alberta",
address = "Edmonton, AB, Canada",
year = "2009",
bibdate = "Sat Nov 12 16:48:00 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.benfordonline.net",
acknowledgement = ack-nhfb,
remark = "According to \cite{Berger:2011:BLS}, the authors'
online bibliography contains more than 600
references.",
}
@InProceedings{Berinde:2009:SOH,
author = "Radu Berinde and Graham Cormode and Piotr Indyk and
Martin J. Strauss",
title = "Space-optimal heavy hitters with strong error bounds",
crossref = "Paredaens:2009:PTE",
pages = "157--166",
year = "2009",
DOI = "http://doi.acm.org/10.1145/1559795.1559819",
bibdate = "Thu Jul 2 14:05:34 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "The problem of finding heavy hitters and approximating
the frequencies of items is at the heart of many
problems in data stream analysis. It has been observed
that several proposed solutions to this problem can
outperform their worst-case guarantees on real data.
This leads to the question of whether some stronger
bounds can be guaranteed. We answer this in the
positive by showing that a class of `counter-based
algorithms' (including the popular and very
space-efficient FREQUENT and SPACESAVING algorithms)
provide much stronger approximation guarantees than
previously known. Specifically, we show that errors in
the approximation of individual elements do not depend
on the frequencies of the most frequent elements, but
only on the frequency of the remaining `tail.' This
shows that counter-based methods are the most
space-efficient (in fact, space-optimal) algorithms
having this strong error bound.\par
This tail guarantee allows these algorithms to solve
the `sparse recovery' problem. Here, the goal is to
recover a faithful representation of the vector of
frequencies, $f$. We prove that using space $ O(k) $,
the algorithms construct an approximation $ f* $ to the
frequency vector $f$ so that the L1 error $ ||f -
f*||_1 $ is close to the best possible error $ \hbox
{min}_{f_2} || f_2 - f ||_1 $, where $f$ 2 ranges over
all vectors with at most $k$ non-zero entries. This
improves the previously best known space bound of about
$ O(k \log n) $ for streams without element deletions
(where $n$ is the size of the domain from which stream
elements are drawn). Other consequences of the tail
guarantees are results for skewed (Zipfian) data, and
guarantees for accuracy of merging multiple summarized
streams.",
acknowledgement = ack-nhfb,
keywords = "frequency estimation; heavy hitters; streaming
algorithms",
}
@Article{Blasius:2009:ZLP,
author = "Bernd Blasius and Ralf T{\"o}njes",
title = "{Zipf's Law} in the Popularity Distribution of Chess
Openings",
journal = j-PHYS-REV-LET,
volume = "103",
number = "21",
pages = "218701",
day = "16",
month = nov,
year = "2009",
CODEN = "PRLTAO",
DOI = "http://dx.doi.org/10.1103/PhysRevLett.103.218701",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.103.218701",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
pagecount = "4",
}
@Article{Bradley:2009:WBL,
author = "Jonathan R. Bradley and David L. Farnsworth",
title = "What Is {Benford's Law}?",
journal = "Teaching Statistics",
volume = "31",
number = "1",
pages = "2--6",
month = jan,
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.1111/j.1467-9639.2009.00347.x",
ISSN = "0141-982X (print), 1467-9639 (electronic)",
ISSN-L = "0141-982X",
bibdate = "Mon Nov 14 17:09:33 MST 2011",
bibsource = "http://onlinelibrary.wiley.com/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Class activity; First significant digit; Goodness of
fit; Teaching",
onlinedate = "6 Jan 2009",
}
@InProceedings{Burns:2009:SSR,
author = "B. D. Burns",
editor = "N. Taatgen and H. van Rijn",
booktitle = "{Proceedings of the Thirty-First Annual Conference of
the Cognitive Science Society, Cognitive Science
Society, Austin, TX}",
title = "Sensitivity to Statistical Regularities: People
(Largely) Follow {Benford's Law}",
publisher = "????",
address = "????",
pages = "2872--2877",
year = "2009",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Nov 18 11:57:33 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Chakravorty:2009:TBL,
author = "S. Chakravorty and V. Sridharan",
title = "Testing {Benford's Law} for improving supply chain
decision-making: a field experiment",
journal = j-DRUG-DISCOVERY-TODAY,
volume = "122",
number = "2",
pages = "606--618",
month = dec,
year = "2009",
CODEN = "DDTOFS",
DOI = "http://dx.doi.org/10.1016/j.ijpe.2009.06.017",
ISSN = "1359-6446 (print), 1878-5832 (electronic)",
ISSN-L = "1359-6446",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0925527309002163",
acknowledgement = ack-nhfb,
fjournal = "Drug Discovery Today",
keywords = "Benford's Law",
}
@Article{Chou:2009:BLN,
author = "Mabel C. Chou and Qingxia Kong and Chung-Piaw Teo and
Zuozheng Wang and Huan Zheng",
title = "{Benford's Law} and Number Selection in Fixed-Odds
Numbers Game",
journal = j-J-GAMBL-STUD,
volume = "25",
number = "4",
pages = "503--521",
month = dec,
year = "2009",
CODEN = "JGSTEM",
DOI = "http://dx.doi.org/10.1007/s10899-009-9145-9",
ISSN = "1050-5350 (print), 1573-3602 (electronic)",
ISSN-L = "1050-5350",
bibdate = "Sat Feb 16 15:35:14 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s10899-009-9145-9",
acknowledgement = ack-nhfb,
fjournal = "Journal of Gambling Studies",
}
@Article{Chuang:2009:FPS,
author = "Kun-Ta Chuang and Hung-Leng Chen and Ming-Syan Chen",
title = "Feature-preserved sampling over streaming data",
journal = j-TKDD,
volume = "2",
number = "4",
pages = "15:1--15:??",
month = jan,
year = "2009",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1460797.1460798",
ISSN = "1556-4681 (print), 1556-472X (electronic)",
ISSN-L = "1556-4681",
bibdate = "Fri Apr 24 17:59:51 MDT 2009",
bibsource = "http://www.acm.org/pubs/contents/journals/tkdd/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "In this article, we explore a novel sampling model,
called {\em feature preserved sampling\/} ({\em FPS\/})
that sequentially generates a high-quality sample over
sliding windows. The sampling quality we consider
refers to the degree of consistency between the sample
proportion and the population proportion of each
attribute value in a window. Due to the time-variant
nature of real-world datasets, users are more likely to
be interested in the most recent data. However,
previous works have not been able to generate a
high-quality sample over sliding windows that precisely
preserves up-to-date population characteristics.
Motivated by this shortcoming, we have developed the
{\em FPS\/} algorithm, which has several advantages:
(1) it sequentially generates a sample from a
time-variant data source over sliding windows; (2) the
execution time of {\em FPS\/} is linear with respect to
the database size; (3) the {\em relative\/}
proportional differences between the sample proportions
and population proportions of most distinct attribute
values are guaranteed to be below a specified error
threshold, $ \epsilon $, while the {\em relative\/}
proportion differences of the remaining attribute
values are as close to $ \epsilon $ as possible, which
ensures that the generated sample is of high quality;
(4) the sample rate is close to the user specified rate
so that a high quality sampling result can be obtained
without increasing the sample size; (5) by a thorough
analytical and empirical study, we prove that {\em
FPS\/} has acceptable space overheads, especially when
the attribute values have Zipfian distributions, and
{\em FPS\/} can also excellently preserve the
population proportion of multivariate features in the
sample; and (6) {\em FPS\/} can be applied to infinite
streams and finite datasets equally, and the generated
samples can be used for various applications. Our
experiments on both real and synthetic data validate
that {\em FPS\/} can effectively obtain a high quality
sample of the desired size. In addition, while using
the sample generated by {\em FPS\/} in various mining
applications, a significant improvement in efficiency
can be achieved without compromising the model's
precision.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Knowledge Discovery from Data
(TKDD)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1054",
keywords = "sampling; Streaming mining",
}
@Article{Clauset:2009:PLDc,
author = "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
Newman",
title = "Power-Law Distributions in Empirical Data",
journal = j-SIAM-REVIEW,
volume = "51",
number = "4",
pages = "661--703",
month = "????",
year = "2009",
CODEN = "SIREAD",
DOI = "http://dx.doi.org/10.1137/070710111",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Mon May 17 17:56:49 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/51/4;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Docampo:2009:BLA,
author = "Silvia Docampo and Mar{\'\i}a {del Mar Trigo} and
Mar{\'\i}a Aira and Baltasar Cabezudo and Antonio
Flores-Moya",
title = "{Benford}'s law applied to aerobiological data and its
potential as a quality control tool",
journal = j-AEROBIOLOGIA,
volume = "25",
number = "4",
pages = "275--283",
month = dec,
year = "2009",
CODEN = "AROBFT",
DOI = "http://dx.doi.org/10.1007/s10453-009-9132-8",
ISSN = "0393-5965 (print), 1573-3025 (electronic)",
ISSN-L = "0393-5965",
bibdate = "Fri Nov 25 10:47:33 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.ingentaconnect.com/content/klu/aero/2009/00000025/00000004/00009132",
acknowledgement = ack-nhfb,
fjournal = "Aerobiologia",
}
@Article{Dorfleitner:2009:PBE,
author = "Gregor Dorfleitner and Christian Klein",
title = "Psychological barriers in {European} stock markets:
Where are they?",
journal = j-GLOB-FINANCE-J,
volume = "19",
number = "3",
pages = "268--285",
month = oct,
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/j.gfj.2008.09.001",
ISSN = "1044-0283 (print), 1873-5665 (electronic)",
ISSN-L = "1044-0283",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S1044028308000549",
abstract = "We examine four European stock indices and the prices
of eight major German stocks for indications of
psychological barriers. The frequency, (expected)
returns, intraday volatility and trading volume of
these assets are studied contingent on whether the
prices lie within a certain range around round numbers.
Our results indicate that psychological barriers do not
exist on a consistent basis. It seems that some
barriers have disappeared after these anomalies have
been published. This discovery is consistent with
current literature findings about disappearing stock
market anomalies.",
acknowledgement = ack-nhfb,
fjournal = "Global Finance Journal",
keywords = "Benford's Law; Disappearing anomalies; M-values;
Psychological barriers",
}
@Article{Fewster:2009:SEB,
author = "Rachel M. Fewster",
title = "A Simple Explanation of {Benford's Law}",
journal = j-AMER-STAT,
volume = "63",
number = "1",
pages = "26--32",
month = feb,
year = "2009",
CODEN = "ASTAAJ",
DOI = "http://dx.doi.org/10.1198/tast.2009.0005",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRnumber = "2655700",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://pubs.amstat.org/doi/pdfplus/10.1198/tast.2009.0005",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Gauvrit:2009:LBG,
author = "Nicolas Gauvrit and Jean-Paul Delahaye",
title = "Loi de {Benford} g{\'e}n{\'e}rale. ({French})
[{General} {Benford}'s law]",
journal = "Math. Sci. Hum. Math. Soc. Sci.",
volume = "??",
number = "186",
pages = "5--15",
year = "2009",
CODEN = "????",
ISSN = "0987-6936 (print), 1950-6821 (electronic)",
ISSN-L = "0987-6936",
MRclass = "62E10 (11A63 37A45)",
MRnumber = "2562062 (2010i:62029)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://msh.revues.org/document11034.html",
acknowledgement = ack-nhfb,
fjournal = "Math{\'e}matiques et Sciences Humaines. Mathematics
and Social Sciences",
language = "French",
}
@Article{Gauvrit:2009:SRI,
author = "N. Gauvrit and J.-P. Delahaye",
title = "Scatter and regularity imply {Benford}'s law \ldots{}
and more",
journal = "ArXiv e-prints",
month = oct,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009arXiv0910.1359G;
http://arxiv.org/abs/0910.1359",
abstract = "A random variable (r.v.) $X$ is said to follow
Benford's law if $ \log (X) $ is uniform $ \bmod 1 $.
Many experimental data sets prove to follow an
approximate version of it, and so do many mathematical
series and continuous random variables. This phenomenon
received some interest, and several explanations have
been put forward. Most of them focus on specific data,
depending on strong assumptions, often linked with the
log function. Some authors hinted --- implicitly ---
that the two most important characteristics of a random
variable when it comes to Benford are regularity and
scatter. In a first part, we prove two theorems, making
up a formal version of this intuition: scattered and
regular r.v.'s do approximately follow Benford's law.
The proofs only need simple mathematical tools, making
the analysis easy. Previous explanations thus become
corollaries of a more general and simpler one. These
results suggest that Benford's law does not depend on
properties linked with the log function. We thus
propose and test a general version of the Benford's
law. The success of these tests may be viewed as an a
posteriori validation of the analysis formulated in the
first part.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0910.1359",
keywords = "Mathematics - Probability, Statistics - Methodology,
G.3",
primaryclass = "math.PR",
}
@Article{Gisin:2009:EEV,
author = "Vladimir Gisin and Andrey Markov and Igor Vinukov",
title = "Estimation of extreme values of returns using the
{Zipf--Mandelbrot} flow",
journal = j-INT-J-PURE-APPL-MATH,
volume = "50",
number = "2",
pages = "245--250",
year = "2009",
CODEN = "????",
ISSN = "1311-8080",
ISSN-L = "1314-3395",
MRclass = "60G70 (91B28 91B84)",
MRnumber = "2488836",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Pure and Applied
Mathematics",
journal-URL = "http://ijpam.eu/",
}
@TechReport{Gonzales-Garcia:2009:BLM,
author = "J. Gonzales-Garcia and G. Pastor",
title = "{Benford's Law} and Macroeconomic Data Quality",
type = "Working Paper",
institution = "International Monetary Fund",
address = "????",
year = "2009",
bibdate = "Tue Nov 22 18:53:16 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1356437",
acknowledgement = ack-nhfb,
}
@Article{Gunnel:2009:DBL,
author = "S. G{\"u}nnel and K.-H. T{\"o}dter",
title = "Does {Benford's Law} Hold in Economic Research and
Forecasting?",
journal = j-EMPIRICA,
volume = "36",
number = "3",
pages = "273--292",
month = aug,
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.1007/s10663-008-9084-1",
ISSN = "0340-8744 (print), 1573-6911 (electronic)",
ISSN-L = "0340-8744",
bibdate = "Thu Nov 17 19:16:10 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.springerlink.com/content/100261/",
abstract = "First and higher order digits in data sets of natural
and socio-economic processes often follow a
distribution called Benford's law. This phenomenon has
been used in business and scientific applications,
especially in fraud detection for financial data. In
this paper, we analyse whether Benford's law holds in
economic research and forecasting. First, we examine
the distribution of regression coefficients and
standard errors in research papers, published in
Empirica and Applied Economics Letters. Second, we
analyse forecasts of GDP growth and CPI inflation in
Germany, published in Consensus Forecasts. There are
two main findings: The relative frequencies of the
first and second digits in economic research are
broadly consistent with Benford's law. In sharp
contrast, the second digits of Consensus Forecasts
exhibit a massive excess of zeros and fives, raising
doubts on their information content.",
acknowledgement = ack-nhfb,
fjournal = "Empirica",
}
@Article{Hales:2009:TBL,
author = "Douglas N. Hales and Satya S. Chakravorty and V.
Sridharan",
title = "Testing {Benford's Law} for improving supply chain
decision-making: A field experiment",
journal = j-INT-J-PROD-ECON,
volume = "122",
number = "2",
pages = "606--618",
month = dec,
year = "2009",
CODEN = "JPCEYE",
DOI = "http://dx.doi.org/10.1016/j.ijpe.2009.06.017",
ISSN = "0925-5273 (print), 1873-7579 (electronic)",
ISSN-L = "0925-5273",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0925527309002163",
abstract = "Supply chain managers must often trust data reported
from suppliers to make decisions about sourcing and
product reliability due to the costs or complexity of
implementing traditional monitoring systems. Without
some form of monitoring, these types of data are
vulnerable to manipulation, thus making their
suitability for decision-making ambiguous and creating
an opportunity for supplier opportunism . Recent
practitioner literature suggests one solution to this
problem they refer to as trust-but-verify . The purpose
of this empirical study is to scientifically examine
the feasibility and cost of implementing one
trust-but-verify method in a real-world supply chain
using a principle called Benford's Law. The results of
this two-year study suggest that the technique is
feasible and cost effective in identifying supply chain
data that have been intentionally manipulated. This
finding can allow supply chain managers to segregate
suspect data from decision-making until they can be
validated and thus mitigate supplier opportunism.",
acknowledgement = ack-nhfb,
ajournal = "Int. j. prod. econ.",
fjournal = "International Journal of Production Economics",
keywords = "Benford's Law; Digital analysis; Operations
management; Supplier opportunism; Supply chain
management",
}
@Article{Hartshorn:2009:BRB,
author = "Kevin Hartshorn",
title = "Book Review: {{\booktitle{The fabulous Fibonacci
numbers}} by Alfred Posamentier and Ingmar Lehmann}",
journal = j-J-MATH-ARTS,
volume = "3",
number = "2",
pages = "113--116",
month = "????",
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/17513470902897569",
ISSN = "1751-3472 (print), 1751-3480 (electronic)",
ISSN-L = "1751-3480",
bibdate = "Sat Jan 07 09:43:47 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/17513470902897569",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematics and the Arts",
onlinedate = "05 Jun 2009",
}
@Article{Hernando:2009:ZLF,
author = "A. Hernando and D. Puigdom{\`e}nech and D. Villuendas
and C. Vesperinas and A. Plastino",
title = "{Zipf}'s law from a {Fisher} variational-principle",
journal = j-PHYS-LET-A,
volume = "374",
number = "1",
pages = "18--21",
day = "14",
month = dec,
year = "2009",
CODEN = "PYLAAG",
DOI = "http://dx.doi.org/10.1016/j.physleta.2009.10.027",
ISSN = "0375-9601 (print), 1873-2429 (electronic)",
ISSN-L = "0375-9601",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0375960109012894",
acknowledgement = ack-nhfb,
fjournal = "Physics Letters A",
journal-URL = "http://www.sciencedirect.com/science/journal/03759601",
keywords = "Zipf's Law",
}
@InCollection{Horgan:2009:BL,
author = "Jane M. Horgan",
title = "{Benford's Law}",
crossref = "Horgan:2009:PRI",
chapter = "9.4",
pages = "142--144",
year = "2009",
bibdate = "Mon Feb 18 18:46:16 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Hurlimann:2009:GBL,
author = "Werner H{\"u}rlimann",
title = "Generalizing {Benford}'s law using power laws:
application to integer sequences",
journal = j-INT-J-MATH-MATH-SCI,
pages = "10",
year = "2009",
CODEN = "????",
ISSN = "0161-1712",
ISSN-L = "0161-1712",
MRclass = "60E05 (11B83 62E15)",
MRnumber = "2533550 (2010h:60043)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Article ID 970284.",
URL = "http://arxiv.org/abs/math/0607166",
abstract = "A simple method to derive parametric analytical
extensions of Benford's law for first digits of
numerical data is proposed. Two generalized Benford
distributions are considered, namely the two-sided
power Benford distribution and the new Pareto Benford
distribution. The fitting capabilities of these
generalized Benford distributions are illustrated and
compared at some interesting and important integer
sequences.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematics and Mathematical
Sciences",
}
@Article{Jang:2009:CDH,
author = "D. Jang and J. U. Kang and A. Kruckman and J. Kudo and
S. J. Miller",
title = "Chains of distributions, hierarchical {Bayesian}
models and {Benford's Law}",
journal = "Journal of Algebra, Number Theory: Advances and
Applications",
volume = "1",
number = "1",
pages = "37--60",
month = mar,
year = "2009",
CODEN = "????",
ISSN = "0972-5555",
ISSN-L = "0972-5555",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0805.4226",
keywords = "Mathematics - Probability, Mathematics - Statistics
Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)",
primaryclass = "math.PR",
}
@Article{Janvresse:2009:BL,
author = "Elise Janvresse and Thierry de la Rue",
title = "{Benford}'s law",
journal = "Butl. Soc. Catalana Mat.",
volume = "24",
number = "1",
pages = "5--12",
year = "2009",
CODEN = "????",
ISSN = "0214-316X",
ISSN-L = "0214-316X",
MRclass = "62-01",
MRnumber = "2567485",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Translated by Frederic Utzet",
acknowledgement = ack-nhfb,
fjournal = "Butllet{\'\i}n de la Societat Catalana de
Matem{\`a}tiques",
}
@Article{Jin:2009:AUR,
author = "Jang C. Jin",
title = "{Asian} University Rankings in International and
Development Economics: An Application of {Zipf's Law}",
journal = j-REV-INT-ECON,
volume = "17",
number = "1",
pages = "137--143",
year = "2009",
DOI = "http://dx.doi.org/10.1111/j.1467-9396.2008.00790.x",
ISSN = "0965-7576 (print), 1467-9396 (electronic)",
ISSN-L = "0965-7576",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Review of International Economics",
}
@Article{Jin:2009:PME,
author = "Jang C. Jin",
title = "Publications in mathematical economics and
econometrics: ranking of {Asian} universities and an
application of {Zipf's Law}",
journal = "{Asian-Pacific} Economic Literature",
volume = "23",
number = "2",
pages = "116--122",
year = "2009",
DOI = "http://dx.doi.org/10.1111/j.1467-8411.2009.01233.x",
ISSN = "0818-9935 (print), 1467-8411 (electronic)",
ISSN-L = "0818-9935",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/%28ISSN%291467-8411",
}
@Article{Jolissaint:2009:LBR,
author = "Paul Jolissaint",
title = "Loi de {Benford}, relations de r{\'e}currence et
suites {\'e}quidistribu{\'e}es. {II}. ({French})
[{Benford}'s Law, recurrence relations, and
equidistributed sequences. {II}]",
journal = j-ELEM-MATH,
volume = "64",
number = "1",
pages = "21--36",
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.4171/EM/112",
ISSN = "0013-6018 (print), 1420-8962 (electronic)",
ISSN-L = "0013-6018",
MRclass = "62E10 (11A63 37A45)",
MRnumber = "2471593 (2010f:62032)",
MRreviewer = "Denys Pommeret",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Elemente der Mathematik",
language = "French",
}
@Article{Judge:2009:DPS,
author = "G. Judge and L. Schechter",
title = "Detecting Problems in Survey Data using {Benford's
Law}",
journal = j-J-HUM-RESOUR,
volume = "44",
number = "1",
pages = "1--24",
month = "Winter",
year = "2009",
CODEN = "JHREA9",
DOI = "http://dx.doi.org/10.3368/jhr.44.1.1",
ISSN = "0022-166X (print), 1548-8004 (electronic)",
ISSN-L = "0022-166X",
bibdate = "Tue Nov 22 18:55:52 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jhr.uwpress.org/content/44/1/1.abstract;
http://www.ssc.wisc.edu/jhr/2009ab/judge1.htm",
acknowledgement = ack-nhfb,
fjournal = "Journal of Human Resources",
}
@Article{Kafri:2009:DNE,
author = "Oded Kafri",
title = "The Distributions in Nature and Entropy Principle",
journal = "ArXiv e-prints",
day = "28",
month = jul,
year = "2009",
bibdate = "Mon Nov 21 07:26:11 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/0907.4852",
abstract = "The derivation of the maximum entropy distribution of
particles in boxes yields two kinds of distributions: a
``bell-like'' distribution and a long-tail
distribution. The first one is obtained when the ratio
between particles and boxes is low, and the second one
when the ratio is high. The obtained long tail
distribution yields correctly the empirical Zipf law,
Pareto's 20:80 rule and Benford's law. Therefore, it is
concluded that the long tail and the ``bell-like''
distributions are outcomes of the tendency of
statistical systems to maximize entropy.",
acknowledgement = ack-nhfb,
pagecount = "19",
}
@Article{Kafri:2009:EPD,
author = "Oded Kafri",
title = "Entropy Principle in Direct Derivation of {Benford's
Law}",
journal = "ArXiv e-prints",
month = jan,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009arXiv0901.3047K;
http://arxiv.org/abs/0901.3047",
abstract = "The uneven distribution of digits in numerical data,
known as Benford's law, was discovered in 1881. Since
then, this law has been shown to be correct in copious
numerical data relating to economics, physics and even
prime numbers. Although it attracts considerable
attention, there is no a priori probabilistic criterion
when a data set should or should not obey the law. Here
a general criterion is suggested, namely that any file
of digits in the Shannon limit (namely, having maximum
entropy) has a Benford's law distribution of digits.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0901.3047",
keywords = "Computer Science - Discrete Mathematics, Physics -
Data Analysis, Statistics and Probability",
primaryclass = "cs.DM",
}
@Article{Kim:2009:ITA,
author = "Hyo-Jeong Kim and Michael Mannino and Robert J.
Nieschwietz",
title = "Information technology acceptance in the internal
audit profession: Impact of technology features and
complexity",
journal = j-INT-J-ACCOUNT-INFO-SYS,
volume = "10",
number = "4",
pages = "214--228",
year = "2009",
CODEN = "IJAIA7",
DOI = "http://dx.doi.org/10.1016/j.accinf.2009.09.001",
ISSN = "1467-0895",
ISSN-L = "1467-0895",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Ninth International Research Symposium on Accounting
Information Systems (IRSAIS)",
URL = "http://www.sciencedirect.com/science/article/pii/S1467089509000360",
abstract = "Although various information technologies have been
studied using the technology acceptance model (TAM),
the study of acceptance of specific technology features
for professional groups employing information
technologies such as internal auditors (IA) has been
limited. To address this gap, we extended the {TAM} for
technology acceptance among {IA} professionals and
tested the model using a sample of internal auditors
provided by the Institute of Internal Auditors (IIA).
System usage, perceived usefulness, and perceived ease
of use were tested with technology features and
complexity. Through the comparison of {TAM} variables,
we found that technology features were accepted by
internal auditors in different ways. The basic features
such as database queries, ratio analysis, and audit
sampling were more accepted by internal auditors while
the advanced features such as digital analysis,
regression/ANOVA, and classification are less accepted
by internal auditors. As feature complexity increases,
perceived ease of use decreased so that system usage
decreased. Through the path analysis between {TAM}
variables, the results indicated that path magnitudes
were significantly changed by technology features and
complexity. Perceived usefulness had more influence on
feature acceptance when basic features were used, and
perceived ease of use had more impact on feature
acceptance when advanced features were used.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Accounting Information
Systems",
keywords = "Benford's Law; Information technology adoption;
Internal auditing; System acceptance; {IS} features",
}
@Article{Krakar:2009:ABL,
author = "Mario {\v{Z}}gela and Zdravko Krakar",
title = "Application of {Benford's Law} in Payment System
Auditing",
journal = j-J-INFO-ORG-SCI,
volume = "33",
number = "1",
pages = "39--51",
month = "????",
year = "2009",
CODEN = "????",
ISSN = "1846-3312 (print), 1846-9418 (electronic)",
ISSN-L = "1846-3312",
bibdate = "Sun Nov 13 11:12:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://bib.irb.hr/datoteka/457819.04_Application_of_Benford_s_Law_in_Payment_Systems_Auditing1.pdf;
http://jios.foi.hr/index.php/jios/article/view/108/66;
http://jios.foi.hr/index.php/jios/issue/view/13",
acknowledgement = ack-nhfb,
fjournal = "Journal of Informational and Organizational Sciences",
journal-URL = "http://jios.foi.hr/index.php/jios/index",
xxjournal = "Journal of Information Ethics and Organisational
Science (wrong!)",
}
@Article{Lansey:2009:ISR,
author = "Jonathan C. Lansey and Bruce Bukiet",
title = "{Internet} Search Result Probabilities: {Heaps' Law}
and Word Associativity",
journal = j-J-QUANT-LINGUISTICS,
volume = "16",
number = "1",
pages = "40--66",
month = "????",
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/09296170802514153",
ISSN = "0929-6174 (print), 1744-5035 (electronic)",
ISSN-L = "0929-6174",
bibdate = "Sat Jan 07 09:36:17 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/09296170802514153",
abstract = "We study the number of internet search results
returned from multi-word queries based on the number of
results returned when each word is searched for
individually. We derive a model to describe search
result values for multi-word queries using the total
number of pages indexed by Google and by applying the
Zipf power law to the words per page distribution on
the internet and Heaps' law for unique word counts.
Based on data from 351 word pairs each with exactly one
hit when searched for together, and a Zipf law
coefficient determined in other studies, we approximate
the Heaps' law coefficient for the indexed worldwide
web (about 8 billion pages) to be $ \beta = 0.52 $.
Previous studies used under 20,000 pages. We
demonstrate through examples how the model can be used
to analyse automatically the relatedness of word pairs
assigning each a value we call ``strength of
associativity''. We demonstrate the validity of our
method with word triplets and through two experiments
conducted 8 months apart. We then use our model to
compare the index sizes of competing search giants
Yahoo and Google.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Quantitative Linguistics",
keywords = "Benford's Law; Heaps' Law; Zipf's Law",
onlinedate = "25 Feb 2009",
remark = "From page 65: ``We mention that tests we have
conducted show that internet searches for random
numbers return approximately log-normally distributed
results and sorting by first digits yields results that
follow Benford's law (1938).''",
}
@Article{Li:2009:PDD,
author = "Weihai Li and Yuan Yuan and Nenghai Yu",
title = "Passive detection of doctored {JPEG} image via block
artifact grid extraction",
journal = j-SIG-PROC,
volume = "89",
number = "9",
pages = "1821--1829",
year = "2009",
CODEN = "SPRODR",
DOI = "http://dx.doi.org/10.1016/j.sigpro.2009.03.025",
ISSN = "0165-1684",
ISSN-L = "0165-1684",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165168409001315",
abstract = "It has been noticed that the block artifact grids
(BAG), caused by the blocking processing during {JPEG}
compression, are usually mismatched when interpolating
or concealing objects by copy paste operations. In this
paper, the {BAGs} are extracted blindly with a new
extraction algorithm, and then abnormal {BAGs} can be
detected with a marking procedure. Then the phenomenon
of grid mismatch or grid blank can be taken as a trail
of such forensics. Experimental results show that our
method can mark these trails efficiently.",
acknowledgement = ack-nhfb,
fjournal = "Signal Processing",
keywords = "Benford's Law; Block artifact grid; Doctored image
forensic; Grid mismatch; {JPEG} compression",
}
@Article{Lipovetsky:2009:PLD,
author = "Stan Lipovetsky",
title = "{Pareto} $ 80 / 20 $ law: derivation via random
partitioning",
journal = j-INT-J-MATH-EDU-SCI-TECH,
volume = "40",
number = "2",
pages = "271--277",
month = "????",
year = "2009",
CODEN = "IJMEBM",
DOI = "http://dx.doi.org/10.1080/00207390802213609",
ISSN = "0020-739X (print), 1464-5211 (electronic)",
ISSN-L = "0020-739X",
bibdate = "Sat Jan 07 09:22:31 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00207390802213609",
abstract = "The Pareto 80/20 Rule, also known as the Pareto
principle or law, states that a small number of causes
(20\%) is responsible for a large percentage (80\%) of
the effect. Although widely recognized as a heuristic
rule, this proportion has not been theoretically based.
The article considers derivation of this 80/20 rule and
some other standard quotients from the mean and its
interval estimation for the total value defined by the
product of two variables in the random partitioning
model.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematical Education in
Science and Technology",
onlinedate = "19 Feb 2009",
}
@Article{Luque:2009:FDF,
author = "Bartolo Luque and Lucas Lacasa",
title = "The first digit frequencies of prime numbers and
{Riemann} zeta zeros",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
volume = "465",
number = "2107",
pages = "2197--2216",
day = "8",
month = jul,
year = "2009",
CODEN = "PRLAAZ",
DOI = "http://dx.doi.org/10.1098/rspa.2009.0126",
ISSN = "1364-5021 (print), 1471-2946 (electronic)",
ISSN-L = "1364-5021",
bibdate = "Mon Feb 25 10:44:43 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://rspa.royalsocietypublishing.org/content/465/2107/2197.abstract",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society A: Mathematical,
Physical, \& Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
keywords = "Benford's Law",
onlinedate = "22 April 2009",
}
@Article{Mahdian:2009:UNI,
author = "Babak Mahdian and Stanislav Saic",
title = "Using noise inconsistencies for blind image
forensics",
journal = j-IMAGE-VIS-COMPUT,
volume = "27",
number = "10",
pages = "1497--1503",
year = "2009",
CODEN = "IVCODK",
DOI = "http://dx.doi.org/10.1016/j.imavis.2009.02.001",
ISSN = "0262-8856",
ISSN-L = "0262-8856",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/cryptography2000.bib",
note = "Special Section: Computer Vision Methods for Ambient
Intelligence",
URL = "http://www.sciencedirect.com/science/article/pii/S0262885609000146",
abstract = "A commonly used tool to conceal the traces of
tampering is the addition of locally random noise to
the altered image regions. The noise degradation is the
main cause of failure of many active or passive image
forgery detection methods. Typically, the amount of
noise is uniform across the entire authentic image.
Adding locally random noise may cause inconsistencies
in the image's noise. Therefore, the detection of
various noise levels in an image may signify tampering.
In this paper, we propose a novel method capable of
dividing an investigated image into various partitions
with homogeneous noise levels. In other words, we
introduce a segmentation method detecting changes in
noise level. We assume the additive white Gaussian
noise. Several examples are shown to demonstrate the
proposed method's output. An extensive quantitative
measure of the efficiency of the noise estimation part
as a function of different noise standard deviations,
region sizes and various {JPEG} compression qualities
is proposed as well.",
acknowledgement = ack-nhfb,
fjournal = "Image and Vision Computing",
keywords = "Benford's Law; Digital forgery; Image forensics; Image
segmentation; Image tampering; Noise inconsistency",
}
@TechReport{Moller:2009:MQA,
author = "M. M{\"o}ller",
title = "Measuring the Quality of Auditing Services with the
Help of {Benford's Law} -- An Empirical Analysis and
Discussion of this Methodical Approach",
type = "Report",
number = "??",
institution = "Institute for Accounting and Control, University of
Z{\"u}rich",
address = "Z{\"u}rich, Switzerland",
pages = "25",
day = "24",
month = apr,
year = "2009",
bibdate = "Tue Nov 22 20:40:12 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://ssrn.com/abstract=1529307",
abstract = "The so-called Benford's Law describes regularity in
the distribution of digits of randomly selected
numbers, which states that the relative frequency of
the leading digits reduces in a systematic manner from
the digit 1 to the digit 9. This distribution
hypothesis is being discussed in recent times as an
audit instrument in order to gain insights into
possible conscious and inadvertent errors in data
records. The present paper analyses the closing
accounts of 1,373 annual financial statements of
companies listed on the German DAX and compares these
with the Benford's distribution hypothesis. It can be
seen in the process that data pertaining to financial
accounts, which have not been audited by the so-called
``Big 4'' audit firms, but by smaller external
auditors, deviate to a significant extent from the
regularity of Benford's Law, which appears to make the
use of Benford's Law suitable as a benchmark to assess
the quality of the audit.",
acknowledgement = ack-nhfb,
}
@Article{Moret:2009:GSA,
author = "M. A. Moret and V. de Senna and M. C. Santana and G.
F. Zebende",
title = "Geometric Structural Aspects of Proteins and
{Newcomb--Benford Law}",
journal = j-INT-J-MOD-PHYS-C,
volume = "20",
number = "12",
pages = "1981--1988",
month = "????",
year = "2009",
CODEN = "IJMPEO",
DOI = "http://dx.doi.org/10.1142/S0129183109014874",
ISSN = "0129-1831 (print), 1793-6586 (electronic)",
ISSN-L = "0129-1831",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009IJMPC..20.1981M",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Modern Physics C [Physics and
Computers]",
journal-URL = "http://www.worldscientific.com/loi/ijmpc",
keywords = "Hydrophobicity, protein packing, complex systems, Time
series analysis, Systems obeying scaling laws, Binary
and multiple stars",
}
@Article{Ni:2009:BLD,
author = "Dong-Dong Ni and Lai Wei and Zhong-Zhou Ren",
title = "{Benford's Law} and $ \beta $-Decay Half-Lives",
journal = j-COMM-THEOR-PHYS,
volume = "51",
number = "4",
pages = "713--716",
month = apr,
year = "2009",
CODEN = "CTPHDI",
DOI = "http://dx.doi.org/10.1088/0253-6102/51/4/25",
ISSN = "0253-6102",
ISSN-L = "0253-6102",
bibdate = "Sun Nov 13 11:01:52 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009CoTPh..51..713N;
http://stacks.iop.org/0253-6102/51/i=4/a=25",
abstract = "The experimental values of 2059 $ \beta $-decay
half-lives are systematically analyzed and
investigated. We have found that they are in
satisfactory agreement with Benford's law, which states
that the frequency of occurrence of each figure, 1--9,
as the first significant digit in a surprisingly large
number of different data sets follows a logarithmic
distribution favoring the smaller ones. Benford's
logarithmic distribution of $ \beta $-decay half-lives
can be explained in terms of Newcomb's justification of
Benford's law and empirical exponential law of $ \beta
$-decay half-lives. Moreover, we test the calculated
values of 6721 $ \beta $-decay half-lives with the aid
of Benford's law. This indicates that Benford's law is
useful for theoretical physicists to test their methods
for calculating $ \beta $-decay half-lives.",
acknowledgement = ack-nhfb,
fjournal = "Communications in theoretical physics",
}
@Article{Nigrini:2009:DDU,
author = "Mark J. Nigrini and Steven J. Miller",
title = "Data Diagnostics Using Second-Order Tests of
{Benford's Law}",
journal = j-AUDITING,
volume = "28",
number = "2",
pages = "305--324",
month = nov,
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.2308/aud.2009.28.2.305",
ISSN = "0278-0380 (print), 1558-7991 (electronic)",
ISSN-L = "0278-0380",
bibdate = "Tue Nov 15 09:11:56 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://aaapubs.org/loi/ajpt;
http://link.aip.org/link/AJPTXX/v28/i2/p305/s1",
abstract = "Auditors are required to use analytical procedures to
identify the existence of unusual transactions, events,
and trends. Benford's Law gives the expected patterns
of the digits in numerical data, and has been advocated
as a test for the authenticity and reliability of
transaction level accounting data. This paper describes
a new second-order test that calculates the digit
frequencies of the differences between the ordered
(ranked) values in a data set. These digit frequencies
approximate the frequencies of Benford's Law for most
data sets. The second-order test is applied to four
sets of transactional data. The second-order test
detected errors in data downloads, rounded data, data
generated by statistical procedures, and the inaccurate
ordering of data. The test can be applied to any data
set and nonconformity usually signals an unusual issue
related to data integrity that might not have been
easily detectable using traditional analytical
procedures",
acknowledgement = ack-nhfb,
fjournal = "Auditing: A Journal of Practice \& Theory",
}
@InCollection{Nisbet:2009:CFD,
author = "Robert Nisbet and John Elder and Gary Miner",
booktitle = "Handbook of Statistical Analysis and Data Mining
Applications",
title = "Chapter 17 --- Fraud Detection",
publisher = "Academic Press",
address = "Boston",
pages = "347--361",
year = "2009",
DOI = "http://dx.doi.org/10.1016/B978-0-12-374765-5.00017-6",
ISBN = "0-12-374765-1",
ISBN-13 = "978-0-12-374765-5",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/B9780123747655000176",
abstract = "Fraud can be defined as a criminal activity, involving
false representations to gain an unjust advantage. It
occurs in a wide variety of forms and is ever changing
as new technologies and new economic and social systems
provide new opportunities for fraudulent activity. This
chapter introduces fraud detection, provides a simple
example of how to build a fraud model, and directs one
to additional references to broaden and deepen the
knowledge of the vast scope of fraud detection. Fraud
is a form of human response that can be modeled in ways
very similar to customer response in business. The
temporal dimension of fraud provides a rich source of
information related to fraud. The occurrence of a fraud
event at a given time may be highly related to the
pattern of events that happened in the past. These
historical data are the most important source of
attributes needed to sufficiently define the fraud
signature in the data set. Fraud modeling requires the
construction of reference objects based on
relationships that are drawn in the past between
various conditions and the incidence of fraud. The
basic approach to fraud detection with an analytical
model is to identify possible predictors of fraud
associated with known fraudsters and their actions in
the past. The most powerful fraud models are built on
historical data.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Rajabpour:2009:SRC,
author = "M. A. Rajabpour and S. M. {Vaez Allaei}",
title = "Scaling relations for contour lines of rough
surfaces",
journal = j-PHYS-REV-E,
volume = "80",
number = "1",
pages = "011115",
day = "13",
month = jul,
year = "2009",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.80.011115",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.80.011115",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Romero-Rochin:2009:DBL,
author = "V. Romero-Rochin",
title = "A derivation of {Benford's Law} \ldots{} and a
vindication of {Newcomb}",
journal = "ArXiv e-prints",
month = sep,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009arXiv0909.3822R;
http://arxiv.org/abs/0909.3822",
abstract = "We show how Benford's Law (BL) for first, second,
\ldots{}, digits, emerges from the distribution of
digits of numbers of the type $ a^R $, with $a$ any
real positive number and $R$ a set of real numbers
uniformly distributed in an interval $ [P \log_a(10),
(P + 1) \log_a(10)) $ for any integer $P$. The result
is shown to be number base and scale invariant. A rule
based on the mantissas of the logarithms allows for a
determination of whether a set of numbers obeys BL or
not. We show that BL applies to numbers obtained from
the {\it multiplication\/} or {\it division\/} of
numbers drawn from any distribution. We also argue that
(most of) the real-life sets that obey BL are because
they are obtained from such basic arithmetic
operations. We exhibit that all these arguments were
discussed in the original paper by Simon Newcomb in
1881, where he presented Benford's Law.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0909.3822",
keywords = "Mathematics - Probability, Mathematics - History and
Overview",
pagecount = "12",
primaryclass = "math.PR",
}
@Article{Roukema:2009:BLA,
author = "B. F. Roukema",
title = "{Benford's Law} anomalies in the 2009 {Iranian}
presidential election",
journal = "ArXiv e-prints",
month = jun,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009arXiv0906.2789R;
http://arxiv.org/abs/0906.2789",
abstract = "The vote count first digit frequencies of the 2009
Iranian presidential election are analysed assuming
proportionality of candidates' votes to the total vote
per voting area. This method is closely related to
Benford's Law. A highly significant ($ p \approx 0.0007
$ ) excess of vote counts for candidate $K$ that start
with the digit 7 is found (41 observed, 21.2--22
expected). Using this property as a selection criterion
leads to the following coincidences. (i) Among the six
most populous voting areas, this criterion selects
those three that have greater proportions of votes for
A than the other three. The probability that the two
sub-groups are drawn from the same distribution is $ p
\approx 0.1 $. (ii) $K$'s vote counts for these same
three voting areas all have the same second digit. The
probability of this is $ p \approx 0.01 $. (iii) Most
(75\%) of the vote counts for $K$ in voting areas with
70 to 79 votes for $K$ are odd, and every even number
occurs exactly once. The probability of the latter is $
p \approx 0.0005 $. Interpreting the big city effect
(i) +( ii) as an overestimate of the true vote, assumed
to be roughly 50\% to match other data, while retaining
constant total vote numbers and increasing votes for
the other three candidates in proportion to their
average voting percentages, would imply that the
difference between A's and M's vote totals would drop
by about one million votes. These results do not
exclude other anomalies.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0906.2789",
keywords = "Statistics - Applications",
primaryclass = "stat.AP",
}
@Article{Sambridge:2009:ABL,
author = "M. Sambridge and H. Tkalcic and A. Jackson",
title = "On the applicability of {Benford's Law} in the
Geosciences",
journal = "AGU Fall Meeting Abstracts",
pages = "A1756--??",
month = dec,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:32:38 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009AGUFM.S33A1756S",
acknowledgement = ack-nhfb,
keywords = "[1294] GEODESY AND GRAVITY / Instruments and
techniques, [1594] GEOMAGNETISM AND PALEOMAGNETISM /
Instruments and techniques, [3294] MATHEMATICAL
GEOPHYSICS / Instruments and techniques, [7299]
SEISMOLOGY / General or miscellaneous",
}
@Article{Shao:2009:FDD,
author = "Lijing Shao and Bo-Qiang Ma",
title = "First digit distribution of hadron full width",
journal = j-MOD-PHYS-LETT-A,
volume = "24",
number = "40",
pages = "3275--3282",
month = "????",
year = "2009",
CODEN = "MPLAEQ",
DOI = "http://dx.doi.org/10.1142/S0217732309031223",
ISSN = "0217-7323 (print), 1793-6632 (electronic)",
ISSN-L = "0217-7323",
bibdate = "Mon Nov 14 16:26:06 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "A phenomenological law, called Benford's law, states
that the occurrence of the first digit, i.e., $ 1, 2,
\ldots {}, 9 $, of numbers from many real world sources
is not uniformly distributed, but instead favors
smaller ones according to a logarithmic distribution.
We investigate, for the first time, the first digit
distribution of the full widths of mesons and baryons
in the well defined science domain of particle physics
systematically, and find that they agree excellently
with the Benford distribution. We also discuss several
general properties of Benford's law, i.e., the law is
scale-invariant, base-invariant, and power-invariant.
This means that the lifetimes of hadrons follow also
Benford's law.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1004.3077",
fjournal = "Modern Physics Letters A (MPLA)",
primaryclass = "hep-ph",
}
@Article{Shi:2009:FDL,
author = "Yun Q. Shi",
title = "{First Digit Law} and Its Application to Digital
Forensics",
journal = j-LECT-NOTES-COMP-SCI,
volume = "5450",
pages = "448--453",
year = "2009",
CODEN = "LNCSD9",
DOI = "http://dx.doi.org/10.1007/978-3-642-04438-0_37",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Jan 21 17:32:48 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/lncs.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-04438-0_37",
acknowledgement = ack-nhfb,
book-DOI = "http://dx.doi.org/10.1007/978-3-642-04438-0",
book-URL = "http://www.springerlink.com/content/978-3-642-04438-0",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Speed:2009:YWP,
author = "T. Speed",
title = "You want proof?",
journal = j-BULL-INST-MATH-STAT,
volume = "38",
number = "??",
pages = "11--??",
month = "????",
year = "2009",
CODEN = "SMBCVA",
ISSN = "0146-3942",
ISSN-L = "0146-3942",
bibdate = "Wed Nov 16 07:00:01 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://bulletin.imstat.org/archive/",
acknowledgement = ack-nhfb,
fjournal = "Bulletin --- Institute of Mathematical Statistics",
keywords = "Benford's Law",
remark = "As of 16 November 2011, volume 38 is not yet online at
the publisher Web site, although there are (broken)
links for volumes 31 (2002) to date.",
}
@Article{Stosic:2009:CSM,
author = "Borko D. Stosi{\'c} and Tatijana Stosi{\'c}",
title = "Comment on {``Ising model on the scale-free network
with a Cayley-tree-like structure''}",
journal = j-PHYS-REV-E,
volume = "79",
number = apr,
pages = "048101",
day = "24",
month = apr,
year = "2009",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.79.048101",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.79.048101",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
pagecount = "2",
}
@Misc{Tao:2009:BLZ,
author = "Terrence Tao",
title = "{Benford}'s law, {Zipf}'s law, and the {Pareto}
distribution",
howpublished = "Web document.",
year = "2009",
bibdate = "Mon Nov 14 16:59:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-law-and-the-pareto-distribution/",
acknowledgement = ack-nhfb,
}
@Article{Todter:2009:BLI,
author = "Karl-Heinz T{\"o}dter",
title = "{Benford's Law} as an Indicator of Fraud in
Economics",
journal = j-GER-ECON-REV,
volume = "10",
number = "3",
pages = "339--351",
month = aug,
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.1111/j.1468-0475.2009.00475.x",
ISSN = "1465-6485 (print), 1468-0475 (electronic)",
ISSN-L = "1465-6485",
bibdate = "Mon Nov 14 17:09:33 MST 2011",
bibsource = "http://onlinelibrary.wiley.com/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "German Economic Review",
onlinedate = "16 Jun 2009",
}
@Article{Xie:2009:FAS,
author = "Tao Xie and Yao Sun",
title = "A file assignment strategy independent of workload
characteristic assumptions",
journal = j-TOS,
volume = "5",
number = "3",
pages = "10:1--10:??",
month = nov,
year = "2009",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1629075.1629079",
ISSN = "1553-3077 (print), 1553-3093 (electronic)",
ISSN-L = "1553-3077",
bibdate = "Tue Mar 16 15:33:57 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/tos/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/tos.bib",
abstract = "The problem of statically assigning nonpartitioned
files in a parallel I/O system has been extensively
investigated. A basic workload characteristic
assumption of most existing solutions to the problem is
that there exists a strong inverse correlation between
file access frequency and file size. In other words,
the most popular files are typically small in size,
while the large files are relatively unpopular. Recent
studies on the characteristics of Web proxy traces
suggested, however, the correlation, if any, is so weak
that it can be ignored. Hence, the following two
questions arise naturally. First, can existing
algorithms still perform well when the workload
assumption does not hold? Second, if not, can one
develop a new file assignment strategy that is immune
to the workload assumption? To answer these questions,
we first evaluate the performance of three well-known
file assignment algorithms with and without the
workload assumption, respectively. Next, we develop a
novel static nonpartitioned file assignment strategy
for parallel I/O systems, called static round-robin
(SOR), which is immune to the workload assumption.
Comprehensive experimental results show that SOR
consistently improves the performance in terms of mean
response time over the existing schemes.",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Storage",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J960",
keywords = "File assignment; load balancing; parallel I/O;
workload characteristics; Zipfian distribution",
}
@Article{Zhang:2009:ZDT,
author = "Jianhua Zhang and Qinghua Chen and Yougui Wang",
title = "{Zipf} distribution in top {Chinese} firms and an
economic explanation",
journal = j-PHYSICA-A,
volume = "388",
number = "10",
pages = "2020--2024",
day = "15",
month = may,
year = "2009",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2009.01.027",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437109000806",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Article{Abourbih:2010:SSD,
author = "Jonathan A. Abourbih and Luke Blaney and Alan Bundy
and Fiona McNeill",
title = "A Single-Significant-Digit Calculus for Semi-Automated
Guesstimation",
journal = j-LECT-NOTES-COMP-SCI,
volume = "6173",
pages = "354--368",
year = "2010",
CODEN = "LNCSD9",
DOI = "http://dx.doi.org/10.1007/978-3-642-14203-1_31",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Jan 21 17:43:23 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/lncs.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-14203-1_31",
acknowledgement = ack-nhfb,
book-DOI = "http://dx.doi.org/10.1007/978-3-642-14203-1",
book-URL = "http://www.springerlink.com/content/978-3-642-14203-1",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Misc{Alagoz:2010:MDB,
author = "Ali Alag{\"o}z and Mustafa Ay",
title = "Muhasebe Denetiminde {Benford} Kanunu Temelli Dijital
Analiz. ({Turkish}) [{Benford Law}-Based Digital
Analysis of Accounting Oversight]",
pages = "17",
day = "8",
month = jan,
year = "2010",
bibdate = "Mon Feb 18 09:19:01 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "www.alialagoz.com.tr/doc-dr-alialagoz-makaleleri/muhasebe_denetiminde_benfrod_kanunu_temelli_dijital_analiz.pdf",
acknowledgement = ack-nhfb,
language = "Turkish",
}
@Article{Aldous:2010:WCO,
author = "David Aldous and Tung Phan",
title = "When Can One Test an Explanation? {Compare} and
Contrast {Benford's Law} and the Fuzzy {CLT}",
journal = j-AMER-STAT,
volume = "64",
number = "3",
pages = "221--227",
month = aug,
year = "2010",
CODEN = "ASTAAJ",
DOI = "http://dx.doi.org/10.1198/tast.2010.09098",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRnumber = "2757166",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1198/tast.2010.09098",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Altamirano:2010:PTS,
author = "Carlo Altamirano and Alberto Robledo",
title = "Possible thermodynamic structure underlying the laws
of {Zipf} and {Benford}",
journal = "ArXiv e-prints",
day = "10",
month = aug,
year = "2010",
bibdate = "Mon Nov 21 07:12:08 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1008.1614",
abstract = "We show that the laws of Zipf and Benford, obeyed by
scores of numerical data generated by many and diverse
kinds of natural phenomena and human activity are
related to the focal expression of a generalized
thermodynamic structure. This structure is obtained
from a deformed type of statistical mechanics that
arises when configurational phase space is incompletely
visited in a severe way. Specifically, the restriction
is that the accessible fraction of this space has
fractal properties. The focal expression is an
(incomplete) Legendre transform between two entropy (or
Massieu) potentials that when particularized to first
digits leads to a previously existing generalization of
Benford's law. The inverse functional of this
expression leads to Zipf's law; but it naturally
includes the bends or tails observed in real data for
small and large rank. Remarkably, we find that the
entire problem is analogous to the transition to chaos
via intermittency exhibited by low-dimensional
nonlinear maps. Our results also explain the generic
form of the degree distribution of scale-free
networks.",
acknowledgement = ack-nhfb,
remark = "To be published in European Physical Journal B.",
}
@Article{Anderson:2010:BLC,
author = "Theresa Anderson and Larry Rolen and Ruth Stoehr",
title = "{Benford's} Law For Coefficients of Modular Forms and
Partition Functions",
journal = "ArXiv e-prints",
day = "3",
month = sep,
year = "2010",
bibdate = "Mon Nov 21 07:10:51 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1009.0780",
abstract = "Here we prove that Benford's law holds for
coefficients of an infinite class of modular forms.
Expanding the work of Bringmann and Ono on exact
formulas for harmonic Maass forms, we derive the
necessary asymptotics. This implies that the
unrestricted partition function $ p(n) $, as well as
other natural partition functions, satisfy Benford's
law.",
acknowledgement = ack-nhfb,
pagecount = "10",
}
@Article{Bachmann:2010:APC,
author = "Val{\'e}rie Bachmann and Martin H. Fischer and
Hans-Peter Landolt and Peter Brugger",
title = "Asymmetric prefrontal cortex functions predict
asymmetries in number space",
journal = j-BRAIN-COGN,
volume = "74",
number = "3",
pages = "306--311",
month = dec,
year = "2010",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/j.bandc.2010.08.011",
ISSN = "0278-2626 (print), 1090-2147 (electronic)",
ISSN-L = "0278-2626",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0278262610001272",
acknowledgement = ack-nhfb,
fjournal = "Brain and Cognition",
keywords = "Benford's Law; small-number bias (SNB); Spatial
Numerical Association of Response Codes (SNARC)
effect",
}
@Article{Balanzario:2010:SCB,
author = "Eugenio P. Balanzario and Jorge S{\'a}nchez-Ortiz",
title = "Sufficient conditions for {Benford's Law}",
journal = j-STAT-PROB-LETT,
volume = "80",
number = "23--24",
pages = "1713--1719",
day = "1--15",
month = dec,
year = "2010",
CODEN = "SPLTDC",
DOI = "http://dx.doi.org/10.1016/j.spl.2010.07.014",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "62E10 (62E17)",
MRnumber = "2734233 (2011i:62019)",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715210002087",
abstract = "We present two sufficient conditions for an absolutely
continuous random variable to obey Benford's Law for
the distribution of the first significant digit. These
two sufficient conditions suggest that Benford's Law
will not often be observed in everyday sets of
numerical data. On the other hand, we recall that there
are two processes by way of which a random variable can
come close to following Benford's Law. The first of
these is the multiplication of independent random
variables and the second is the exponentiation of a
random variable to a large power. Our working tool is
the Poisson sum formula of Fourier analysis. Like the
central limit theorem, Benford's Law has an asymptotic
nature.",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Benford's Law; First significant digit",
}
@Article{Balaz:2010:BLD,
author = "V. Bal{\'a}{\v{z}} and K. Nagasaka and O. Strauch",
title = "{Benford}'s law and distribution functions of
sequences in $ (0, 1) $",
journal = j-MATH-NOTES-ACAD-SCI-USSR,
volume = "88",
number = "3--4",
pages = "449--463",
month = oct,
year = "2010",
CODEN = "MTHNB2",
DOI = "http://dx.doi.org/10.1134/S0001434610090178",
ISSN = "0001-4346 (print), 1573-8876 (electronic)",
ISSN-L = "0001-4346",
bibdate = "Fri Nov 25 10:52:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1134%2FS0001434610090178",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Notes of the {Academy of Sciences of the
USSR = Matematicheskie Zametki}",
}
@Article{Balazh:2010:BLD,
author = "V. Balazh and K. Nagasaka and O. Shtraukh",
title = "{Benford}'s law and distribution functions of
sequences in {$ (0, 1) $}",
journal = j-MAT-ZAMETKI,
volume = "88",
number = "4",
pages = "485--501",
year = "2010",
DOI = "http://dx.doi.org/10.1134/S0001434610090178",
ISSN = "0025-567X",
ISSN-L = "0025-567X",
MRclass = "11K06 (60E05)",
MRnumber = "2882211",
MRreviewer = "Michael Drmota",
bibdate = "Thu Feb 14 07:02:03 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
Zametki",
}
@TechReport{Bauer:2010:DDF,
author = "J. Bauer and J. Gross",
title = "Difficulties Detecting Fraud? {The} Use of {Benford's
Law} on Regression Tables",
type = "Report",
institution = "Institute of Sociology,
Ludwig-Maximilians-Universit{\"a}t",
address = "M{\"u}nchen, Germany",
pages = "????",
year = "2010",
bibdate = "Tue Nov 22 21:15:18 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Beber:2010:WNS,
author = "Bernd Beber and Alexandria Scacco",
title = "What the Numbers Say: a Digit-Based Test for Election
Fraud",
journal = j-POLIT-ANAL,
volume = "20",
number = "2",
pages = "211--234",
month = "Spring",
year = "2010",
DOI = "http://dx.doi.org/10.1093/pan/mps003",
ISSN = "1047-1987 (print), 1476-4989 (electronic)",
ISSN-L = "1047-1987",
bibdate = "Mon Feb 18 17:29:42 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://pan.oxfordjournals.org/content/20/2/211.abstract",
acknowledgement = ack-nhfb,
fjournal = "Political Analysis",
keywords = "Benford's Law",
}
@TechReport{Berger:2010:FFFa,
author = "A. Berger and T. P. Hill",
title = "Fundamental Flaws in {Feller}'s Classical Derivation
of {Benford's Law}",
type = "Preprint",
institution = "Department of Mathematical and Statistical Sciences,
University of Alberta",
address = "Edmonton, AB, Canada",
pages = "8",
year = "2010",
bibdate = "Mon Feb 18 17:31:57 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.benfordonline.net/ARTICLES/BergerHill2010.pdf",
abstract = "Feller's classic text \booktitle{An Introduction to
Probability Theory and its Applications}
\cite{Feller:1968:IPT} contains a derivation of the
well known significant-digit law called Benford's law.
More specifically, Feller gives a sufficient condition
(`large spread') for a random variable $X$ to be
approximately Benford distributed, that is, for $
\log_{10} X $ to be approximately uniformly distributed
modulo one. This note shows that the large-spread
derivation, which continues to be widely cited and
used, contains serious basic errors. Concrete examples
and a new inequality clearly demonstrate that large
spread (or large spread on a logarithmic scale) does
not imply that a random variable is approximately
Benford distributed, for any reasonable definition of
`spread' or measure of dispersion.",
acknowledgement = ack-nhfb,
}
@Article{Berger:2010:FFFb,
author = "Arno Berger and Theodore P. Hill",
title = "Fundamental Flaws in {Feller}'s Classical Derivation
of {Benford's Law}",
journal = "ArXiv e-prints",
month = may,
year = "2010",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 18:23:13 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1005.2598B;
http://arxiv.org/abs/1005.2598",
abstract = "Feller's classic text \booktitle{An Introduction to
Probability Theory and its Applications}
\cite{Feller:1968:IPT} contains a derivation of the
well known significant-digit law called Benford's law.
More specifically, Feller gives a sufficient condition
(`large spread') for a random variable $X$ to be
approximately Benford distributed, that is, for $
\log_{10}X $ to be approximately uniformly distributed
modulo one. This note shows that the large-spread
derivation, which continues to be widely cited and
used, contains serious basic errors. Concrete examples
and a new inequality clearly demonstrate that large
spread (or large spread on a logarithmic scale) does
not imply that a random variable is approximately
Benford distributed, for any reasonable definition of
`spread' or measure of dispersion",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1005.2598",
keywords = "Mathematics - Probability, Mathematics - Statistics,
62Axx",
primaryclass = "math.PR",
}
@TechReport{Berger:2010:LSD,
author = "A. Berger",
title = "Large Spread Does Not Imply {Benford's Law}",
type = "Preprint",
institution = "Department of Mathematical and Statistical Sciences,
University of Alberta",
address = "Edmonton, AB, Canada",
year = "2010",
bibdate = "Sat Nov 12 16:46:10 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.math.ualberta.ca/~aberger/Publications.html",
acknowledgement = ack-nhfb,
}
@Article{Block:2010:GEB,
author = "Henry W. Block and Thomas H. Savits",
title = "A General Example for {Benford} Data",
journal = j-AMER-STAT,
volume = "64",
number = "4",
pages = "335--339",
month = nov,
year = "2010",
CODEN = "ASTAAJ",
DOI = "http://dx.doi.org/10.1198/tast.2010.09169",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRnumber = "2758565",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Benford's Law deals, among other things, with the
proportion of numbers whose first significant digit is
a $1$ (e.g., $ 0.00131 $ and $ 19668 $ both have first
significant digit $1$ ) in a variety of datasets. In
these datasets, which arise in various compendiums or
as mixtures of various sets of numbers, the proportion
of numbers with first significant digit one is $ 0.3010
$ which is much higher than the commonsense value of $
1 / 9 $. The reasons for this occurrence have been
elusive. Mathematical attempts to explain this
phenomenon have been relatively fruitless. Methods
involving probability have been somewhat more
successful. In this article we give some simple reasons
for this occurrence and also give an example of a
general mixture of distributions which exactly
satisfies this Law. Various other examples and
counterexamples are also given.",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Bonache:2010:DFL,
author = "A. B. Bonache and K. Moris and J. Maurice",
title = "{D}{\'e}tection de fraudes et loi de {Benford}:
Quelques risques associ{\'e}s. ({French}) [{Fraud}
detection and {Benford}'s law: Some risks]",
journal = "Revue Fran{\c{c}}aise de Comptabilit{\'e}",
volume = "??",
number = "431",
pages = "24--27",
month = apr,
year = "2010",
CODEN = "????",
DOI = "????",
ISSN = "0484-8764",
ISSN-L = "0484-8764",
bibdate = "Mon Feb 18 17:33:12 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "????",
acknowledgement = ack-nhfb,
journal-URL = "http://www.experts-comptables.fr/csoec/Publications/RFC",
language = "French",
}
@InCollection{Brahler:2010:EMS,
author = "Gernot Br{\"a}hler and Markus Bensmann and Anna-Lena
Emke",
booktitle = "{Ilmenauer Schriften zur Betriebswirtschaftslehre}.
({German}) [{Illmenauer} writings on economics]",
title = "{Der Einsatz mathematisch-statistischer Methoden in
der digitalen Betriebspr{\"u}fung}. ({German}) [{The}
use of mathematical and statistical methods in the
digital audit]",
volume = "4/2010",
publisher = "Verlag proWiWi e.V.",
address = "Ilmenau, Germany",
pages = "48",
month = apr,
year = "2010",
ISBN = "3-940882-23-2",
ISBN-13 = "978-3-940882-23-3",
ISSN = "1866-2145 (print), 2192-4643 (electronic)",
LCCN = "????",
bibdate = "Mon Feb 18 17:35:58 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://www.econstor.eu/dspace/bitstream/10419/55680/1/665348576.pdf",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Bravo-Marquez:2010:HLM,
author = "Felipe Bravo-Marquez and Gaston L'Huillier and
Sebasti{\'a}n A. R{\'\i}os and Juan D. Vel{\'a}squez",
title = "Hypergeometric Language Model and {Zipf}-Like Scoring
Function for {Web} Document Similarity Retrieval",
journal = j-LECT-NOTES-COMP-SCI,
volume = "6393",
pages = "303--308",
year = "2010",
CODEN = "LNCSD9",
DOI = "http://dx.doi.org/10.1007/978-3-642-16321-0_32",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Jan 21 17:49:42 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/lncs.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-16321-0_32",
acknowledgement = ack-nhfb,
book-DOI = "http://dx.doi.org/10.1007/978-3-642-16321-0",
book-URL = "http://www.springerlink.com/content/978-3-642-16321-0",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Burns:2010:PL,
author = "John Burns",
title = "Probably likely",
journal = j-NEW-SCIENTIST,
volume = "208",
number = "2786",
pages = "32-",
year = "2010",
CODEN = "NWSCAL",
DOI = "http://dx.doi.org/10.1016/S0262-4079(10)62810-2",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0262407910628102",
acknowledgement = ack-nhfb,
fjournal = "New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
keywords = "Benford's Law",
}
@Article{Cartlidge:2010:NNO,
author = "Edwin Cartlidge",
title = "In nature, number one dominates",
journal = "Institute of Physics, Environmental Research Letters",
volume = "??",
number = "??",
pages = "??--??",
day = "25",
month = oct,
year = "2010",
DOI = "????",
bibdate = "Mon Feb 18 17:38:16 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://environmentalresearchweb.org/cws/article/news/44124",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Misc{Conway:2010:CFM,
author = "D. Conway",
title = "{Benford's Law} Tests for {Wikileaks} Data",
howpublished = "Zero Intelligence Agents website.",
day = "1",
month = aug,
year = "2010",
bibdate = "Mon Feb 18 17:39:45 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.drewconway.com/zia/?p=2234",
acknowledgement = ack-nhfb,
}
@InCollection{Corazza:2010:CFM,
author = "Marco Corazza and Andrea Ellero and Alberto Zorzi",
booktitle = "Mathematical and statistical methods for actuarial
sciences and finance",
title = "Checking financial markets via {Benford}'s law: the
{S\&P 500} case",
publisher = "Springer Italia",
address = "Milan, Italy",
pages = "93--102",
year = "2010",
DOI = "http://dx.doi.org/10.1007/978-88-470-1481-7_10",
MRclass = "62P05",
MRnumber = "2676191",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Corominas-Murtra:2010:UZL,
author = "Bernat Corominas-Murtra and Ricard V. Sol{\'e}",
title = "Universality of {Zipf}'s law",
journal = j-PHYS-REV-E,
volume = "82",
number = "1",
pages = "011102",
day = "1",
month = jul,
year = "2010",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.82.011102",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
MRclass = "82B03 (62B10)",
MRnumber = "2736361 (2011j:82002)",
MRreviewer = "N. N. Ganikhodjaev",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.82.011102",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
pagecount = "9",
}
@Article{Courtland:2010:CML,
author = "Rachel Courtland",
title = "Curious mathematical law is rife in nature",
journal = j-NEW-SCIENTIST,
volume = "208",
number = "2782",
pages = "10--10",
day = "16",
month = oct,
year = "2010",
CODEN = "NWSCAL",
DOI = "http://dx.doi.org/10.1016/S0262-4079(10)62497-9",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0262407910624979",
abstract = "Disparate data sets produced by natural phenomena all
follow Benford's law, suggesting new ways to detect
earthquakes or scientific anomalies",
acknowledgement = ack-nhfb,
fjournal = "New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
keywords = "Benford's Law; earthquake detection",
xxISSN = "0262-4079, 0028-6664",
}
@InCollection{Crato:2010:MB,
author = "Nuno Crato",
booktitle = "Figuring It Out: Entertaining Encounters with Everyday
Math",
title = "{Mr. Benford}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "173--178",
year = "2010",
CODEN = "LNMAA2",
DOI = "http://dx.doi.org/10.1007/978-3-642-04833-3_41",
ISBN = "3-642-04832-3 (hardcover)",
ISBN-13 = "978-3-642-04832-6 (hardcover)",
bibdate = "Wed Aug 12 09:28:13 MDT 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-04833-3_41.pdf",
abstract = "This is a book of mathematical stories, funny and
puzzling mathematical stories. They tell of villains
who try to steal secrets, heroes who encode their
messages, and mathematicians who spend years on end
searching for the best way to pile oranges. There are
also stories about highway confusions occurring when
the rules of Cartesian geometry are ignored,
small-change errors due to ignorance of ancient
paradoxes, and mistakes in calendars arising from poor
numerical approximations. This book is about the power
and beauty of mathematics. It shows mathematics in
action, explained in a way that everybody can
understand.",
acknowledgement = ack-nhfb,
book-DOI = "http://dx.doi.org/10.1007/978-3-642-04833-3",
bookpages = "ix + 227",
tableofcontents = "Everyday Matters. \\
The dinner table algorithm \\
Cutting the Christmas cake \\
Oranges and computers \\
When two and two don't make four \\
Getting more intelligent every day \\
The other lane always goes faster \\
Shoelaces and neckties \\
Number puzzles \\
Tossing a coin \\
The switch \\
Eubulides, the heap and the Euro \\
The Earth is Round. \\
How GPS works \\
Gear wheels \\
February 29 \\
The Nonius scale \\
Pedro Nunes' map \\
Lighthouse geometry \\
Asteroids and least squares \\
The useful man and the genius \\
Secret Affairs. \\
Alice and Bob \\
Inviolate cybersecrets \\
Quantum cryptography \\
The FBI wavelet \\
The enigma machine \\
Art and Geometry. \\
The Vitruvian man \\
The golden number \\
The geometry of A4 paper sizes \\
The strange worlds of Escher \\
Escher and the M{\"o}bius strip \\
Picasso, Einstein and the fourth dimension \\
Pollock's fractals \\
Voronoi diagrams \\
The Platonic solids \\
Pythagorean mosquitoes \\
The most beautiful of all \\
Mathematical Objects. \\
The power of math \\
Doubts in the realm of certainty \\
When chance enhances reliability \\
The difficulty of chance \\
Conjectures and proofs \\
Mr. Benford \\
Financial fractals \\
Turing's test \\
DNA computers \\
Magical multiplication \\
Pi day \\
The best job in the world \\
Out of This World. \\
Electoral paradoxes \\
The melon paradox \\
The cupcake paradox \\
Infinity \\
Unfair games \\
Monsieur Bertrand \\
Boy or girl? \\
A puzzle for Christmas \\
Crisis time for Easter eggs",
}
@Article{Debreceny:2010:DMJ,
author = "Roger S. Debreceny and Glen L. Gray",
title = "Data mining journal entries for fraud detection: An
exploratory study",
journal = j-INT-J-ACCOUNT-INFO-SYS,
volume = "11",
number = "3",
pages = "157--181",
month = sep,
year = "2010",
CODEN = "IJAIA7",
DOI = "http://dx.doi.org/10.1016/j.accinf.2010.08.001",
ISSN = "1467-0895 (print), 1873-4723 (electronic)",
ISSN-L = "1467-0895",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
note = "See discussion
\cite{Grabski:2010:DDM,Kriel:2010:DDM}.",
URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000540;
http://www.sciencedirect.com/science/journal/14670895",
abstract = "Fraud detection has become a critical component of
financial audits and audit standards have heightened
emphasis on journal entries as part of fraud detection.
This paper canvasses perspectives on applying data
mining techniques to journal entries. In the past, the
impediment to researching journal entry data mining is
getting access to journal entry data sets, which may
explain why the published research in this area is a
null set. For this project, we had access to journal
entry data sets for 29 different organizations. Our
initial exploratory test of the data sets had
interesting preliminary findings. (1) For all 29
entities, the distribution of first digits of journal
dollar amounts differed from that expected by Benford's
Law. (2) Regarding last digits, unlike first digits,
which are expected to have a logarithmic distribution,
the last digits would be expected to have a uniform
distribution. Our test found that the distribution was
not uniform for many of the entities. In fact, eight
entities had one number whose frequency was three times
more than expected. (3) We compared the number of
accounts related to the top five most frequently
occurring three last digit combinations. Four entities
had a very high occurrences of the most frequent three
digit combinations that involved only a small set of
accounts, one entity had a low occurrences of the most
frequent three digit combination that involved a large
set of accounts and 24 had a low occurrences of the
most frequent three digit combinations that involved a
small set of accounts. In general, the first four
entities would probably pose the highest risk of fraud
because it could indicate that the fraudster is
covering up or falsifying a particular class of
transactions. In the future, we will apply more data
mining techniques to discover other patterns and
relationships in the data sets. We also want to seed
the dataset with fraud indicators (e.g., pairs of
accounts that would not be expected in a journal entry)
and compare the sensitivity of the different data
mining techniques to find these seeded indicators.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Accounting Information
Systems",
keywords = "Accounting information systems; Auditing; Benford's
Law; Data mining; Fraud; Journal entries; {XBRL} {GL}",
remark = "2009 Research Symposium on Information Integrity \&
Information Systems Assurance.",
}
@TechReport{Deckert:2010:IBL,
author = "Joseph Deckert and Mikhail Myagkov and Peter C.
Ordeshook",
title = "The Irrelevance of {Benford's Law} for Detecting Fraud
in Elections",
type = "{CALTECH} working paper",
number = "9",
institution = "California Institute of Technology",
address = "Pasadena, CA, USA",
pages = "27",
day = "9",
month = mar,
year = "2010",
bibdate = "Mon Feb 18 17:40:53 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://vote.caltech.edu/drupal/node/327",
acknowledgement = ack-nhfb,
remark = "From the abstract: ``..., we argue here that Benford's
Law is essentially useless as a forensic indicator of
fraud.''",
}
@Article{Deligny:2010:RRL,
author = "H. Deligny and P. Jolissaint",
title = "Relations de r{\'e}currence lin{\'e}aires,
primitivit{\'e} et loi de {Benford}. ({French})
[{Linear} recurrence relations, primitivity, and
{Benford's Law}]",
journal = "ArXiv e-prints",
day = "23",
month = jul,
year = "2010",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 18:14:51 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1007.5349D;
http://arxiv.org/abs/1007.5349",
abstract = "We prove that many sequences of positive numbers $
(a_n) $ defined by finite linear difference equations $
a_{n + k} = c_{k - 1} a_{n + k - 1} + \ldots {} + c_0
a_n $ with suitable nonnegative reals coefficients $
c_i $ satisfy Benford's Law on the first digit in many
bases $ b > 2 $. Our techniques rely on
Perron--Frobenius theory via the companion matrix of
the characteristic polynomial of the defining
equation.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1007.5349",
keywords = "Mathematics - Dynamical Systems, Mathematics - Rings
and Algebras, 11A99",
language = "French",
primaryclass = "math.DS",
}
@Article{Diekmann:2010:BLF,
author = "Andreas Diekmann and Ben Jann",
title = "{Benford's Law} and Fraud Detection: Facts and
Legends",
journal = j-GER-ECON-REV,
volume = "11",
number = "3",
pages = "397--401",
month = aug,
year = "2010",
CODEN = "????",
DOI = "http://dx.doi.org/10.1111/j.1468-0475.2010.00510.x",
ISSN = "1465-6485 (print), 1468-0475 (electronic)",
ISSN-L = "1465-6485",
bibdate = "Mon Nov 14 17:09:33 MST 2011",
bibsource = "http://onlinelibrary.wiley.com/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "German Economic Review",
keywords = "Benford's law; false negative; false positive; fraud
detection; regression coefficients",
onlinedate = "6 Apr 2010",
}
@Article{Egghe:2010:NSP,
author = "Leo Egghe",
title = "A new short proof of {Naranan}'s theorem, explaining
{Lotka's Law} and {Zipf's Law}",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "61",
number = "12",
pages = "2581--2583",
year = "2010",
CODEN = "JASIEF",
DOI = "http://dx.doi.org/10.1002/asi.21431",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
}
@Article{Farkas:2010:SUN,
author = "Janos Farkas and Gy{\"o}rgy Gyurky",
title = "The significance of using the {Newcomb--Benford} law
as a test of nuclear half-life calculations",
journal = "Acta Physica Polonica, B",
volume = "41",
pages = "1213--1221",
year = "2010",
CODEN = "APOBBB",
ISSN = "0587-4254 (print), 1509-5770 (electronic)",
ISSN-L = "0587-4254",
bibdate = "Mon Nov 14 16:21:42 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1006.3615F;
http://arxiv.org/abs/1006.3615",
abstract = "Half-life number sequences collected from nuclear data
charts are found to obey the Newcomb--Benford law.
Based on this fact, it has been suggested recently,
that this law should be used to test the quality of
nuclear decay models. In this paper we briefly recall
how, when and why the Newcomb--Benford law can be
observed in a set of numbers with a given probability
distribution. We investigate the special case of
nuclear half-lives, and show that the law provides no
additional clue in understanding decay half-lives.
Thus, it can play no significant role in testing
nuclear decay theories.",
acknowledgement = ack-nhfb,
ajournal = "Acta Phys. Pol. B",
ajournal-2 = "Acta Phys. Polon. B",
archiveprefix = "arXiv",
eprint = "1006.3615",
primaryclass = "math-ph",
}
@Article{Ferrer-i-Cancho:2010:RTD,
author = "Ramon Ferrer-i-Cancho and Brita Elvev{\aa}g",
title = "Random Texts Do Not Exhibit the Real {Zipf's Law}-Like
Rank Distribution",
journal = j-PLOS-ONE,
volume = "5",
number = "3",
pages = "e9411:1--e9411:10",
month = mar,
year = "2010",
CODEN = "POLNCL",
DOI = "http://dx.doi.org/10.1371/journal.pone.0009411",
ISSN = "1932-6203",
bibdate = "Wed Aug 12 08:54:42 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0009411",
abstract = "Zipf's law states that the relationship between the
frequency of a word in a text and its rank (the most
frequent word has rank 1, the 2nd most frequent word
has rank 2, \ldots{}) is approximately linear when
plotted on a double logarithmic scale. It has been
argued that the law is not a relevant or useful
property of language because simple random texts ---
constructed by concatenating random characters
including blanks behaving as word delimiters ---
exhibit a Zipf's law-like word rank distribution.",
acknowledgement = ack-nhfb,
fjournal = "PLoS One",
journal-URL = "http://www.plosone.org/",
}
@Article{Fischer:2010:HCS,
author = "Martin H. Fischer and Richard A. Mills and Samuel
Shaki",
title = "How to cook a {SNARC}: Number placement in text
rapidly changes spatial-numerical associations",
journal = j-BRAIN-COGN,
volume = "72",
number = "3",
pages = "333--336",
month = apr,
year = "2010",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/j.bandc.2009.10.010",
ISSN = "0278-2626 (print), 1090-2147 (electronic)",
ISSN-L = "0278-2626",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0278262609002024",
abstract = "Most theoreticians believe that reading habits explain
why Western adults associate small numbers with left
space and large numbers with right space (the {SNARC}
effect). We challenge this belief by documenting, in
both English and Hebrew, that {SNARC} changes during
reading: small and large numbers in our texts appeared
near the left or right ends of the lines, positioned
either spatially congruent or incongruent with reading
habits. In English, the congruent group showed reliable
{SNARC} before and after reading and the incongruent
group's {SNARC} was significantly reduced. In Hebrew
the incongruent reading condition even induced a
reverse SNARC. These results show that {SNARC} is a
fleeting aspect of number representation that captures
multiple spatial associations.",
acknowledgement = ack-nhfb,
fjournal = "Brain and Cognition",
keywords = "Benford's Law; Number line; Numerical cognition;
Reading; Spatial Numerical Association of Response
Codes (SNARC); Spatial numerical associations; {SNARC}
effect",
}
@Article{Formann:2010:NBL,
author = "Anton K. Formann",
title = "The {Newcomb--Benford Law} in Its Relation to Some
Common Distributions",
journal = j-PLOS-ONE,
volume = "5",
number = "5",
pages = "e10541:1--e10541:13",
month = may,
year = "2010",
CODEN = "POLNCL",
DOI = "http://dx.doi.org/10.1371/journal.pone.0010541",
ISSN = "1932-6203",
ISSN-L = "1932-6203",
bibdate = "Mon Nov 14 18:19:09 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010PLoSO...510541F",
abstract = "An often reported, but nevertheless persistently
striking observation, formalized as the Newcomb-Benford
law (NBL), is that the frequencies with which the
leading digits of numbers occur in a large variety of
data are far away from being uniform. Most spectacular
seems to be the fact that in many data the leading
digit 1 occurs in nearly one third of all cases.
Explanations for this uneven distribution of the
leading digits were, among others, scale- and
base-invariance. Little attention, however, found the
interrelation between the distribution of the
significant digits and the distribution of the observed
variable. It is shown here by simulation that long
right-tailed distributions of a random variable are
compatible with the NBL, and that for distributions of
the ratio of two random variables the fit generally
improves. Distributions not putting most mass on small
values of the random variable (e.g. symmetric
distributions) fail to fit. Hence, the validity of the
NBL needs the predominance of small values and, when
thinking of real-world data, a majority of small
entities. Analyses of data on stock prices, the areas
and numbers of inhabitants of countries, and the
starting page numbers of papers from a bibliography
sustain this conclusion. In all, these findings may
help to understand the mechanisms behind the NBL and
the conditions needed for its validity. That this law
is not only of scientific interest per se, but that, in
addition, it has also substantial implications can be
seen from those fields where it was suggested to be put
into practice. These fields reach from the detection of
irregularities in data (e.g. economic fraud) to
optimizing the architecture of computers regarding
number representation, storage, and round-off errors.",
acknowledgement = ack-nhfb,
fjournal = "PLoS One",
journal-URL = "http://www.plosone.org/",
}
@Article{Genolini:2010:EIP,
author = "Christophe Genolini and Tarak Driss",
title = "Eveiller l'int{\'e}r{\^e}t pour la statistique par
l'exemple. ({French}) [{Raising} interest in statistics
by example]",
journal = "Statistique et Enseignement",
volume = "1",
number = "2",
pages = "49--57",
month = "????",
year = "2010",
CODEN = "????",
DOI = "????",
ISSN = "2108-6745",
ISSN-L = "2108-6745",
bibdate = "Mon Feb 18 17:43:03 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://publications-sfds.math.cnrs.fr/index.php/StatEns/article/view/16",
acknowledgement = ack-nhfb,
journal-URL = "http://www.statistique-et-enseignement.fr/",
keywords = "Benford's Law",
language = "French",
}
@Article{Giuliano:2010:UPI,
author = "Rita Giuliano and {\'E}lise Janvresse",
title = "A unifying probabilistic interpretation of {Benford}'s
law",
journal = "Uniform Distribution Theory",
volume = "5",
number = "2",
pages = "169--182",
year = "2010",
CODEN = "????",
ISSN = "1336-913X",
ISSN-L = "1336-913X",
MRclass = "60J10 (11K99 60A99)",
MRnumber = "2781415",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.boku.ac.at/MATH/udt/vol05/no2/91GiulJan10-2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Unif. Distrib. Theory",
fjournal = "Uniform Distribution Theory",
}
@Article{Grabski:2010:DDM,
author = "Severin Grabski",
title = "Discussion of {``Data mining journal entries for fraud
detection: An exploratory study''}",
journal = j-INT-J-ACCOUNT-INFO-SYS,
volume = "11",
number = "3",
pages = "182--185",
month = sep,
year = "2010",
CODEN = "IJAIA7",
DOI = "http://dx.doi.org/10.1016/j.accinf.2010.07.008",
ISSN = "1467-0895 (print), 1873-4723 (electronic)",
ISSN-L = "1467-0895",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
note = "See \cite{Debreceny:2010:DMJ,Kriel:2010:DDM}.",
URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000394",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Accounting Information
Systems",
keywords = "Benford's Law",
remark = "2009 Research Symposium on Information Integrity \&
Information Systems Assurance",
}
@Article{Herron:2010:EPO,
author = "Erik S. Herron",
title = "The effect of passive observation methods on
{Azerbaijan}'s 2008 presidential election and 2009
referendum",
journal = j-ELECT-STUDIES,
volume = "29",
number = "3",
pages = "417--424",
year = "2010",
DOI = "http://dx.doi.org/10.1016/j.electstud.2010.03.013",
ISSN = "0261-3794",
ISSN-L = "0261-3794",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Special Symposium: Voters and Coalition Governments",
URL = "http://www.sciencedirect.com/science/article/pii/S0261379410000259",
abstract = "Election observation is used by domestic and
international groups to assess election quality and
deter fraud. However, a limited amount of research has
assessed its effectiveness. This article adds to the
literature by analyzing how a passive monitoring tool
affected the process and outcome of voting in two
elections in Azerbaijan. The analysis shows that the
placement of webcams in polling stations is
consistently associated with lower reported turnout and
inconsistently associated with lower regime support.",
acknowledgement = ack-nhfb,
fjournal = "Electoral Studies",
keywords = "Azerbaijan; Benford's Law; Election observation;
Fraud",
}
@Article{Hickman:2010:DAC,
author = "Matthew Hickman and Stephen Rice",
title = "Digital Analysis of Crime Statistics: Does Crime
Conform to {Benford's Law}?",
journal = j-J-QUANT-CRIMINOL,
volume = "26",
number = "3",
pages = "333--349",
month = sep,
year = "2010",
CODEN = "JQCRE6",
DOI = "http://dx.doi.org/10.1007/s10940-010-9094-6",
ISSN = "0748-4518 (print), 1573-7799 (electronic)",
ISSN-L = "0748-4518",
bibdate = "Fri Nov 25 10:30:30 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Quantitative Criminology",
keywords = "Benford distribution; Benford's law; Crime data; Crime
statistics; Data errors; Digital analysis; Fabricated
data; First digit; Fraud detection; Uniform crime
reports",
}
@MastersThesis{Jasak:2010:BZR,
author = "Zoran Jasak",
title = "Benfordov zakon i reinforcement u{\v{c}}enje.
({Bosnian}) [{Benford's Law} and reinforcement
learning]",
type = "{Magistarski Rad} ({M.Sc.} Thesis)",
school = "Prirodno-Matematicki Fakultet, Odsjek za matematiku,
Ju Univerzitet u Tuzla",
address = "Tuzla, Bosnia and Herzegovina",
pages = "124",
month = dec,
year = "2010",
bibdate = "Mon Feb 18 17:48:33 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.math.ualberta.ca/~aberger/benford_bibliography/jasak_10.pdf",
acknowledgement = ack-nhfb,
keywords = "action; Adaptive Benford's method; Adaptivna
Benfordova metoda; akcija; Benford's law; Benfordov
zakon; confidence intervals; contamination level;
intervali povjerenja; koli{\v{c}}nik; nivo
kontaminacije; Q learning; Q u{\v{c}}enje; quotient;
reinforcement learning; reinforcement u{\v{c}}enje;
Sarsa; stanje; state",
language = "Bosnian",
}
@Article{Jiang:2010:NMS,
author = "Weina Jiang and Anthony T. S. Ho and Helen Treharne
and Yun Q. Shi",
title = "A Novel Multi-size Block {Benford's Law} Scheme for
Printer Identification",
journal = j-LECT-NOTES-COMP-SCI,
volume = "6297",
pages = "643--652",
year = "2010",
CODEN = "LNCSD9",
DOI = "http://dx.doi.org/10.1007/978-3-642-15702-8_59",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Jan 21 17:47:23 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/lncs.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-15702-8_59",
acknowledgement = ack-nhfb,
book-DOI = "http://dx.doi.org/10.1007/978-3-642-15702-8",
book-URL = "http://www.springerlink.com/content/978-3-642-15702-8",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Kaynar:2010:FSM,
author = "B. Kaynar and A. Berger and T. P. Hill and A. Ridder",
title = "Finite-state {Markov} Chains obey {Benford's Law}",
journal = "ArXiv e-prints",
month = mar,
year = "2010",
CODEN = "????",
ISSN = "????",
MRclass = "60J22, 11K06, 15B51",
bibdate = "Tue Nov 15 06:30:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1003.0562K;
http://arxiv.org/abs/1003.0562",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1003.0562",
keywords = "Mathematics - Probability",
primaryclass = "math.PR",
}
@Article{Klar:2010:ZLL,
author = "B. Klar and P. R. Parthasarathy and N. Henze",
title = "{Zipf} and {Lerch} limit of birth and death
processes",
journal = j-PROB-ENG-INFO-SCI,
volume = "24",
number = "1",
pages = "129--144",
year = "2010",
CODEN = "????",
DOI = "http://dx.doi.org/10.1017/S0269964809990179",
ISSN = "0269-9648 (print), 1469-8951 (electronic)",
ISSN-L = "0269-9648",
MRclass = "60J27 (91F20)",
MRnumber = "2575846 (2010m:60254)",
bibdate = "Sat Mar 23 12:53:04 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Probab. Engrg. Inform. Sci.",
fjournal = "Probability in the Engineering and Informational
Sciences",
keywords = "Zipf's Law",
}
@Article{Kriel:2010:DDM,
author = "Eckhardt Kriel",
title = "Discussion of {``Data mining journal entries for fraud
detection: An exploratory study''}",
journal = j-INT-J-ACCOUNT-INFO-SYS,
volume = "11",
number = "3",
pages = "186--188",
month = sep,
year = "2010",
CODEN = "IJAIA7",
DOI = "http://dx.doi.org/10.1016/j.accinf.2010.07.009",
ISSN = "1467-0895 (print), 1873-4723 (electronic)",
ISSN-L = "1467-0895",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
note = "See \cite{Debreceny:2010:DMJ,Grabski:2010:DDM}.",
URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000400",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Accounting Information
Systems",
keywords = "Benford's Law",
remark = "2009 Research Symposium on Information Integrity \&
Information Systems Assurance.",
}
@Article{Lee:2010:SAR,
author = "Joanne Lee and Wendy K. Tam Cho and George G. Judge",
title = "{Stigler}'s approach to recovering the distribution of
first significant digits in natural data sets",
journal = j-STAT-PROB-LETT,
volume = "80",
number = "2",
pages = "82--88",
day = "15",
month = jan,
year = "2010",
CODEN = "SPLTDC",
DOI = "http://dx.doi.org/10.1016/j.spl.2009.09.015",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715209003563",
abstract = "Benford's Law can be seen as one of the many first
significant digit (FSD) distributions in a family of
monotonically decreasing distributions. We examine the
interrelationship between Benford and other
monotonically decreasing distributions such as those
arising from Stigler, Zipf, and the power laws. We
examine the theoretical basis of the Stigler
distribution and extend his reasoning by incorporating
{FSD} first-moment information into
information-theoretic methods. We present
information-theoretic methods as a way to describe,
connect, and unify these related distributions and
thereby extend the reach of Benford's Law and {FSD}
research more generally.",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Benford's Law",
}
@Article{Liu:2010:CIE,
author = "Hongyan Liu and Xiaoyu Wang and Yinghui Yang",
title = "Comments on {``An integrated efficient solution for
computing frequent and top-$k$ elements in data
streams''}",
journal = j-TODS,
volume = "35",
number = "2",
pages = "15:1--15:??",
month = apr,
year = "2010",
CODEN = "ATDSD3",
DOI = "http://doi.acm.org/10.1145/1735886.1735894",
ISSN = "0362-5915 (print), 1557-4644 (electronic)",
ISSN-L = "0362-5915",
bibdate = "Wed Apr 28 13:44:08 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/tods/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Metwally:2006:IES}.",
abstract = "We investigate a well-known algorithm, {\em
Space-Saving\/} [Metwally et al. 2006], which has been
proven efficient and effective at mining frequent
elements in data streams. We discovered an error in one
of the theorems in Metwally et al. [2006]. Experiments
are conducted to illustrate the error.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Database Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777",
keywords = "approximate queries; data streams; frequent elements;
top-$k$ elements; Zipfian distributions",
}
@Article{Lu:2010:BLP,
author = "Ocean Fan Lu and David E. Giles",
title = "{Benford's Law} and psychological barriers in certain
{eBay} auctions",
journal = j-APPL-ECON-LETT,
volume = "17",
number = "10",
pages = "1005--1008",
month = "????",
year = "2010",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/13504850802631814",
ISSN = "1350-4851 (print), 1466-4291 (electronic)",
ISSN-L = "1350-4851",
bibdate = "Sat Jan 07 09:10:23 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/13504850802631814",
abstract = "Using generalizations of Benford's Law we test for the
absence of psychological barriers at various price
levels in eBay auctions for professional football
tickets. Our empirical results indicate that this
hypothesis cannot be rejected.",
acknowledgement = ack-nhfb,
fjournal = "Applied Economics Letters",
onlinedate = "16 Jun 2009",
}
@Article{Mahdian:2010:BBM,
author = "Babak Mahdian and Stanislav Saic",
title = "A bibliography on blind methods for identifying image
forgery",
journal = j-SIGNAL-PROCESS-IMAGE-COMMUN,
volume = "25",
number = "6",
pages = "389--399",
month = jul,
year = "2010",
CODEN = "SPICEF",
DOI = "http://dx.doi.org/10.1016/j.image.2010.05.003",
ISSN = "0923-5965 (print), 1879-2677 (electronic)",
ISSN-L = "0923-5965",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0923596510000536",
abstract = "Verifying the integrity of digital images and
detecting the traces of tampering without using any
protecting pre-extracted or pre-embedded information
have become an important and hot research field. The
popularity of this field and the rapid growth in papers
published during the last years have put considerable
need on creating a complete bibliography addressing
published papers in this area. In this paper, an
extensive list of blind methods for detecting image
forgery is presented. By the word blind we refer to
those methods that use only the image function. An
attempt has been made to make this paper complete by
listing most of the existing references and by
providing a detailed classification group.",
acknowledgement = ack-nhfb,
fjournal = "Signal Processing: Image Communication",
keywords = "Benford's Law; Blind forgery detection; Digital
forgery; Image forensics; Image tampering; Multimedia
security",
}
@Article{Manoochehrnia:2010:BLA,
author = "P. Manoochehrnia and F. Rachidi and M. Rubinstein and
W. Schulz and G. Diendorfer",
title = "{Benford's Law} and Its Application to Lightning
Data",
journal = j-IEEE-TRANS-ELECTROMAGN-COMPAT,
volume = "52",
number = "4",
pages = "956--961",
month = nov,
year = "2010",
CODEN = "IEMCAE",
DOI = "http://dx.doi.org/10.1109/TEMC.2010.2067218",
ISSN = "0018-9375 (print), 1558-187X (electronic)",
ISSN-L = "0018-9375",
bibdate = "Mon Nov 21 22:24:43 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electromagnetic Compatibility",
}
@InProceedings{Mebane:2010:EFS,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{2010 Summer Meeting of the Political Methodology
Society, University of Iowa, July 22--24, 2010}",
title = "Election Fraud or Strategic Voting? {Can} Second-digit
Tests Tell the Difference?",
publisher = "????",
address = "????",
pages = "1--49",
year = "2010",
ISBN = "????",
ISBN-13 = "????",
bibdate = "Sat Feb 16 11:56:47 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.umich.edu/~wmebane/pm10.pdf",
acknowledgement = ack-nhfb,
}
@Article{Mebane:2010:FPE,
author = "Walter R. {Mebane, Jr.}",
title = "Fraud in the {2009 Presidential Election} in {Iran}?",
journal = j-CHANCE,
volume = "23",
number = "1",
pages = "6--15",
month = mar,
year = "2010",
CODEN = "CNDCE4",
DOI = "http://dx.doi.org/10.1007/s00144-010-0003-4",
ISSN = "0933-2480 (print), 1867-2280 (electronic)",
ISSN-L = "0933-2480",
bibdate = "Mon Feb 18 17:50:18 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.springerlink.com/content/0337v415563q0753/abstract/",
acknowledgement = ack-nhfb,
fjournal = "Chance: a magazine for people interested in the
analysis of data",
journal-URL = "http://chance.amstat.org/;
http://link.springer.com/journal/144;
http://www.tandfonline.com/loi/ucha20",
xxnote = "Publisher archive at
\path=http://amstat.tandfonline.com/loi/ucha20= is
missing volumes 18 (2005)--24 (2011). Those volumes are
available at
\path=http://link.springer.com/journal/144=",
}
@TechReport{Mebane:2010:MSD,
author = "Walter R. {Mebane, Jr.}",
title = "Memo on second-digit tests done on precinct counts for
{Democratic Senate} primary in {South Carolina}, 2010",
type = "Report",
institution = "University of Michigan",
address = "Ann Arbor, MI, USA",
day = "12",
month = jun,
year = "2010",
bibdate = "Sat Feb 16 12:06:16 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.umich.edu/~wmebane/SCmemo12jun2010.pdf",
acknowledgement = ack-nhfb,
}
@Article{Morrison:2010:MG,
author = "Kent E. Morrison",
title = "The Multiplication Game",
journal = j-MATH-MAG,
volume = "83",
number = "??",
pages = "100--110",
month = apr,
year = "2010",
CODEN = "MAMGA8",
DOI = "????",
ISSN = "0025-570X",
ISSN-L = "0025-570X",
bibdate = "Mon Feb 18 17:51:50 2013",
bibsource = "http://www.maa.org/pubs/mag_apr10_toc.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.calpoly.edu/~kmorriso/Research/multgameMMfinal.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Magazine",
journal-URL = "http://www.maa.org/pubs/mathmag.html",
}
@Book{Newbold:2010:SBE,
author = "Paul Newbold and William L. Carlson and Betty Thorne",
title = "Statistics for Business and Economics",
publisher = "Pearson",
address = "Boston, MA, USA",
edition = "Seventh",
pages = "986 + 16",
year = "2010",
ISBN = "0-13-507248-4",
ISBN-13 = "978-0-13-507248-6",
LCCN = "QA276.18 .N49 2010",
bibdate = "Fri Mar 22 09:03:48 MDT 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
}
@Book{Nillsen:2010:RRD,
author = "Rodney Victor Nillsen",
title = "Randomness and recurrence in dynamical systems: a real
analysis approach",
volume = "31",
publisher = pub-MATH-ASSOC-AMER,
address = pub-MATH-ASSOC-AMER:adr,
pages = "xviii + 357",
year = "2010",
ISBN = "0-88385-043-5",
ISBN-13 = "978-0-88385-043-5",
LCCN = "QA614.8 .N55 2010",
bibdate = "Mon Feb 18 17:53:28 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "The Carus mathematical monographs",
acknowledgement = ack-nhfb,
subject = "Differentiable dynamical systems; Measure theory",
tableofcontents = "Background ideas and knowledge \\
Irrational numbers and dynamical systems \\
Probability and randomness \\
Recurrence \\
Averaging in time and space",
}
@Article{Novikov:2010:APB,
author = "V. P. Novikov",
title = "Aspectual Principle, {Benford's Law} and {Russell's
Paradox}",
journal = "ArXiv e-prints",
month = dec,
year = "2010",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 18:11:57 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1012.5537N;
http://arxiv.org/abs/1012.5537",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1012.5537",
keywords = "Mathematics - Classical Analysis and ODEs",
pagecount = "5",
primaryclass = "math.CA",
}
@Book{Oleksy:2010:DMB,
author = "Marius Oleksy",
title = "{Data Mining und Benford's Law als
Controllinginstrumente}. ({German}) [{Data} Mining and
{Benford's Law} as controlling instruments]",
volume = "45",
publisher = "Europ{\"a}ischer Hochschulverlag",
address = "Bremen, Germany",
pages = "181 (est.)",
year = "2010",
ISBN = "3-86741-405-X",
ISBN-13 = "978-3-86741-405-0",
LCCN = "????",
bibdate = "Mon Feb 18 17:54:59 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "{Wismarer Schriften zu Management und Recht}",
URL = "http://www.amazon.de/Data-Mining-Benfords-Law-Controllinginstrumente/dp/386741405X",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Orita:2010:UBL,
author = "Masaya Orita and Ayako Moritomo and Tatsuya Niimi and
Kazuki Ohno",
title = "Use of {Benford}'s law in drug discovery data",
journal = j-DRUG-DISCOVERY-TODAY,
volume = "15",
number = "9--10",
pages = "328--331",
month = may,
year = "2010",
CODEN = "DDTOFS",
DOI = "http://dx.doi.org/10.1016/j.drudis.2010.03.003",
ISSN = "1359-6446 (print), 1878-5832 (electronic)",
ISSN-L = "1359-6446",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1359644610000796",
abstract = "Benford's law states that the distribution of the
first digit of many data sets is not uniform. The first
digit of any random number will be 1 almost 30\% of the
time, and larger digits occur as the first digit with
lower and lower frequency, to the point where 9 occurs
as a first digit only 5\% of the time. Here, we
demonstrate that several data sets in the field of drug
discovery follow Benford's distribution, whereas
doctored data do not. Our findings indicate the
applicability of Benford's law in assessing data
quality in the field of drug discovery. We also propose
a useful index of evaluating data quality based on
Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "Drug Discovery Today",
keywords = "Benford's Law",
}
@Misc{Pan:2010:EJC,
author = "Da Pan and Lijing Shao and Bo-Qiang Ma",
title = "{Benford's Law} in Statistical Physics",
howpublished = "Wolfram Online Demonstrations Projects.",
year = "2010",
bibdate = "Mon Feb 18 18:00:17 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://demonstrations.wolfram.com/BenfordsLawInStatisticalPhysics/",
acknowledgement = ack-nhfb,
}
@Article{Peng:2010:SFW,
author = "Fei Peng and Re-Si Guo and Chang-Tsun Li and Min
Long",
title = "A semi-fragile watermarking algorithm for
authenticating {$2$D} {CAD} engineering graphics based
on log-polar transformation",
journal = j-COMPUT-AIDED-DES,
volume = "42",
number = "12",
pages = "1207--1216",
year = "2010",
CODEN = "CAIDA5",
DOI = "http://dx.doi.org/10.1016/j.cad.2010.08.004",
ISSN = "0010-4485 (print), 1879-2685 (electronic)",
ISSN-L = "0010-4485",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/cryptography2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010448510001491",
abstract = "Copyright violation and illegal manipulation of
digital data have been acute challenges for many
sectors since the very same set of enabling techniques
for generating and processing digital data started to
emerge. Although traditional protective methods, such
as encryption and digital signatures, have been in use
for decades, their inability to provide protection
after decryption and locating tampering has prompted
the development of digital watermarking. In this paper,
a semi-fragile watermarking algorithm for
authenticating 2D {CAD} engineering graphics based on
log-polar coordinate mapping is proposed. Firstly, the
vertices are divided into groups, and for each group,
the vertices for carrying a watermark are mapped to the
log-polar coordinate system. Then the watermark is
embedded in the mantissa of the real-valued log-polar
coordinates via bit substitution. Theoretical analysis
and experimental results show that the proposed
algorithm is not only robust against incidental global
operations such as rotation, translation and scaling,
but can also detect and locate malicious attacks such
as entity modification and entity addition/deletion.",
acknowledgement = ack-nhfb,
fjournal = "Computer-Aided Design",
journal-URL = "http://www.sciencedirect.com/science/journal/00104485",
keywords = "Benford's Law; Content authentication; Data hiding;
Engineering graphics; Integrity verification;
Semi-fragile watermarking",
}
@Article{Peng:2010:ZLC,
author = "Guohua Peng",
title = "{Zipf}'s law for {Chinese} cities: {Rolling} sample
regressions",
journal = j-PHYSICA-A,
volume = "389",
number = "18",
pages = "3804--3813",
day = "15",
month = sep,
year = "2010",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2010.05.004",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037843711000381X",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Zipf's Law",
}
@Article{Perc:2010:ZLL,
author = "Matja{\v{z}} Perc",
title = "{Zipf}'s law and log-normal distributions in measures
of scientific output across fields and institutions: 40
years of {Slovenia's} research as an example",
journal = j-J-INFORMETRICS,
volume = "4",
number = "3",
pages = "358--364",
day = "1",
month = jul,
year = "2010",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/j.joi.2010.03.001",
ISSN = "1751-1577 (print), 1875-5879 (electronic)",
ISSN-L = "1751-1577",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1751157710000234",
acknowledgement = ack-nhfb,
fjournal = "Journal of Informetrics",
journal-URL = "http://www.sciencedirect.com/science/journal/17511577",
keywords = "Zipf's Law",
}
@Book{Posch:2010:ZNB,
author = "Peter N. Posch",
title = "{Ziffernanalyse mit dem Newcomb--Benford Gesetz in
Theorie und Praxis}. ({German}) [{Digit} analysis with
the {Newcomb--Benford} law in theory and practice]",
publisher = "Verlag Europ{\"a}ische Wirtschaft",
address = "Munich, Germany",
edition = "Second",
pages = "105 (est.)",
year = "2010",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Mon Feb 18 18:01:16 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@InProceedings{Qadir:2010:EJC,
author = "G. Qadir and X. Zhao and A. T. S. Ho",
booktitle = "{Society of Photo-Optical Instrumentation Engineers
(SPIE)} Conference Series",
title = "Estimating {JPEG2000} compression for image forensics
using {Benford's Law}",
volume = "7723",
publisher = pub-SPIE,
address = pub-SPIE:adr,
month = apr,
year = "2010",
DOI = "http://dx.doi.org/10.1117/12.855085",
bibdate = "Mon Nov 14 18:25:16 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Society of Photo-Optical Instrumentation Engineers
(SPIE) Conference Series",
URL = "http://adsabs.harvard.edu/abs/2010SPIE.7723E..14Q",
acknowledgement = ack-nhfb,
}
@Article{Rezayan:2010:SRG,
author = "Hani Rezayan and Mahmoud Reza Delavar and Andrew
Ulrich Frank and A. Mansouri",
title = "Spatial rules that generate urban patterns: Emergence
of the power law in the distribution of axial line
length",
journal = "International Journal of Applied Earth Observation and
Geoinformation",
volume = "12",
number = "5",
pages = "317--330",
year = "2010",
DOI = "http://dx.doi.org/10.1016/j.jag.2010.04.003",
ISSN = "0303-2434",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0303243410000413",
abstract = "This paper studies emergence/generation of power law
in rank-order distribution of axial line length, which
is a global pattern observed in real cities, due to
interaction of a set of seven simple spatial rules at a
local scale. These rules and their interactions form a
model expected to simulate the morphological structure
of free spaces in unplanned organic pedestrian small
cities. Effects of each of the seven rules are
discussed through repeated simulations of eight
possible combinations of the rules, using a bottom-up
process. The results show that the rules generate
environments with statistically stable rank-order
distribution of axial line length that follows the
power law. It means that the axial maps of the
simulated environments have a scale-free hierarchical
structure such that their distributions lean toward
short axial lines. It also represents dominance of
local spatial structure, as the model renders a faster
rate of growth at a local scale while allowing a steady
growth at a global scale.",
acknowledgement = ack-nhfb,
keywords = "Axial line; Axial map; Axial representation; Benford's
Law; Emergence; Power law",
}
@Article{Rousseau:2010:AFO,
author = "Christiane Rousseau",
title = "Apprendre {\`a} frauder ou {\`a} d{\'e}tecter les
fraudes. ({French}) [{Learning} to defraud or to detect
fraud]",
journal = "Accrom$\alpha$th",
volume = "5",
pages = "2--7",
month = "{\'E}t{\'e}--automne",
year = "2010",
ISSN = "1911-0197",
bibdate = "Mon Feb 18 18:07:49 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://accromath.uqam.ca/contents/pdf/Benford.pdf",
acknowledgement = ack-nhfb,
journal-URL = "http://www.accromath.ca/",
language = "French",
}
@Book{Saichev:2010:TZL,
author = "Alexander Saichev and Yannick Malevergne and Didier
Sornette",
title = "Theory of {Zipf}'s law and beyond",
volume = "632",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 171",
year = "2010",
DOI = "http://dx.doi.org/10.1007/978-3-642-02946-2",
ISBN = "3-642-02945-0",
ISBN-13 = "978-3-642-02945-5",
MRclass = "91-02 (91B70 91B82)",
MRnumber = "2569206 (2011b:91008)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Lecture Notes in Economics and Mathematical Systems",
ZMnumber = "Zbl 1189.91009",
acknowledgement = ack-nhfb,
}
@Article{Sambridge:2010:BLN,
author = "M. Sambridge and Hrvoje Tkal{\v{c}}i{\'c} and A.
Jackson",
title = "{Benford}'s law in the natural sciences",
journal = "Geophysical Research Letters",
volume = "37",
number = "22",
pages = "L22301--L22306",
month = "????",
year = "2010",
CODEN = "GPRLAJ",
DOI = "http://dx.doi.org/10.1029/2010GL044830",
ISSN = "0094-8276 (print), 1944-8007 (electronic)",
ISSN-L = "0094-8276",
bibdate = "Sun Nov 13 11:03:47 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010GeoRL..3722301S;
http://www.agu.org/pubs/crossref/2010/2010GL044830.shtml",
abstract = "More than 100 years ago it was predicted that the
distribution of first digits of real world observations
would not be uniform, but instead follow a trend where
measurements with lower first digit (1, 2, \ldots {})
occur more frequently than those with higher first
digits (\ldots {}, 8, 9). This result has long been
known but regarded largely as a mathematical curiosity
and received little attention in the natural sciences.
Here we show that the first digit rule is likely to be
a widespread phenomenon and may provide new ways to
detect anomalous signals in data. We test 15 sets of
modern observations drawn from the fields of physics,
astronomy, geophysics, chemistry, engineering and
mathematics, and show that Benford's law holds for them
all. These include geophysical observables such as the
length of time between geomagnetic reversals, depths of
earthquakes, models of Earth's gravity, geomagnetic and
seismic structure. In addition we find it also holds
for other natural science observables such as the
rotation frequencies of pulsars; green-house gas
emissions, the masses of exoplanets as well as numbers
of infectious diseases reported to the World Health
Organization. The wide range of areas where it is
manifested opens up new possibilities for exploitation.
An illustration is given of how seismic energy from an
earthquake can be detected from just the first digit
distribution of displacement counts on a seismometer,
i.e., without actually looking at the details of a
seismogram at all. This led to the first ever detection
of an earthquake using first digit information alone.",
acknowledgement = ack-nhfb,
ajournal = "Geophys. Res. Lett.",
fjournal = "Geophysical research letters",
keywords = "earthquakes; large data sets; observational
seismology; statistics",
}
@TechReport{Schraepler:2010:BLI,
author = "J{\"o}rg-Peter Schraepler",
title = "{Benford's Law} as an instrument for fraud detection
in surveys using the data of the {Socio-Economic Panel
(SOEP)}",
type = "{SOEP} paper",
number = "273",
institution = "Socio-Economic Panel, Deutsches Institut f{\"u}r
Wirtschaftsforschung",
address = "Berlin, Germany",
pages = "ii + 56",
day = "2",
month = mar,
year = "2010",
ISSN = "1864-6689",
ISSN-L = "1864-6689",
bibdate = "Mon Feb 18 18:10:18 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.diw.de/documents/publikationen/73/diw_01.c.349061.de/diw_sp0273.pdf",
acknowledgement = ack-nhfb,
}
@Article{Shao:2010:EMD,
author = "Lijing Shao and Bo-Qiang Ma",
title = "Empirical Mantissa Distributions of Pulsars",
journal = j-ASTROPART-PHYS,
volume = "33",
number = "4",
pages = "255--262",
month = may,
year = "2010",
CODEN = "APHYEE",
DOI = "http://dx.doi.org/10.1016/j.astropartphys.2010.02.003",
ISSN = "0927-6505 (print), 1873-2852 (electronic)",
ISSN-L = "0927-6505",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1005.1702;
http://www.sciencedirect.com/science/article/pii/S0927650510000447",
abstract = "The occurrence of digits one through nine as the
leftmost nonzero digit of numbers from real world
sources is often not uniformly distributed, but
instead, is distributed according to a logarithmic law,
known as Benford's Law. Here, we investigate
systematically the mantissa distributions of some
pulsar quantities, and find that for most quantities
their first digits conform to this law. However, the
barycentric period shows significant deviation from the
usual distribution, but satisfies a generalized
Benford's Law roughly. Therefore pulsars can serve as
an ideal assemblage to study the first digit
distributions of real world data, and the observations
can be used to constrain theoretical models of pulsar
behavior.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1005.1702",
fjournal = "Astroparticle Physics",
keywords = "Benford's Law; First digit law; Mantissa distribution;
Pulsar",
primaryclass = "astro-ph.IM",
}
@Article{Shao:2010:FDD,
author = "Lijing Shao and Bo-Qiang Ma",
title = "First Digit Distribution of Hadron Full Width",
journal = "ArXiv e-prints",
day = "19",
month = apr,
year = "2010",
bibdate = "Mon Nov 21 07:21:00 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1004.3077",
abstract = "A phenomenological law, called Benford's law, states
that the occurrence of the first digit, i.e., $ 1, 2,
\ldots {}, 9 $, of numbers from many real world sources
is not uniformly distributed, but instead favors
smaller ones according to a logarithmic distribution.
We investigate, for the first time, the first digit
distribution of the full widths of mesons and baryons
in the well defined science domain of particle physics
systematically, and find that they agree excellently
with the Benford distribution. We also discuss several
general properties of Benford's law, i.e., the law is
scale-invariant, base-invariant, and power-invariant.
This means that the lifetimes of hadrons follow also
Benford's law.",
acknowledgement = ack-nhfb,
pagecount = "8",
}
@Article{Shao:2010:FDLa,
author = "Lijing Shao and Bo-Qiang Ma",
title = "First-Digit Law in Nonextensive Statistics",
journal = "ArXiv e-prints",
year = "2010",
bibdate = "Mon Nov 21 07:09:52 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1010.2699",
abstract = "Nonextensive statistics, characterized by a
nonextensive parameter $q$, is a promising and
practically useful generalization of the Boltzmann
statistics to describe power-law behaviors from
physical and social observations. We here explore the
unevenness of the first digit distribution of
nonextensive statistics analytically and numerically.
We find that the first-digit distribution follows
Benford's law and fluctuates slightly in a periodical
manner with respect to the logarithm of the
temperature. The fluctuation decreases when $q$
increases, and the result converges to Benford's law
exactly as $q$ approaches 2. The relevant regularities
between nonextensive statistics and Benford's law are
also presented and discussed.",
acknowledgement = ack-nhfb,
}
@Article{Shao:2010:FDLb,
author = "Lijing Shao and Bo-Qiang Ma",
title = "First-digit law in nonextensive statistics",
journal = j-PHYS-REV-E,
volume = "82",
number = "4",
pages = "041110",
month = oct,
year = "2010",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.82.041110",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Mon Feb 18 18:11:37 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.82.041110;
http://pre.aps.org/abstract/PRE/v82/i4/e041110",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
}
@Article{Shao:2010:SDL,
author = "Lijing Shao and Bo-Qiang Ma",
title = "The significant digit law in statistical physics",
journal = j-PHYSICA-A,
volume = "389",
number = "16",
pages = "3109--3116",
month = may,
year = "2010",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2010.04.021",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "82B03",
MRnumber = "2652860 (2011d:82007)",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1005.0660;
http://inspirehep.net/record/855898;
http://inspirehep.net/record/873155;
http://www.sciencedirect.com/science/article/pii/S0378437110003596",
abstract = "The occurrence of the nonzero leftmost digit, i.e., $
1, 2, \ldots {}, 9 $, of numbers from many real world
sources is not uniformly distributed as one might
naively expect, but instead, the nature favors smaller
ones according to a logarithmic distribution, named
Benford's law. We investigate three kinds of widely
used physical statistics, i.e., the Boltzmann--Gibbs
(BG) distribution, the Fermi--Dirac (FD) distribution,
and the Bose--Einstein (BE) distribution, and find that
the BG and FD distributions both fluctuate slightly in
a periodic manner around the Benford distribution with
respect to the temperature of the system, while the BE
distribution conforms to it exactly whatever the
temperature is. Thus the Benford's law seems to present
a general pattern for physical statistics and might be
even more fundamental and profound in nature.
Furthermore, various elegant properties of Benford's
law, especially the mantissa distribution of data sets,
are discussed.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Benford's Law; First digit law; Mantissa distribution;
Statistical physics",
}
@Article{Shebaro:2010:LTC,
author = "Bilal Shebaro and Fernando Perez-Gonzalez and Jedidiah
R. Crandall",
title = "Leaving timing-channel fingerprints in hidden service
log files",
journal = "Digital Investigation",
volume = "7, Supplement",
number = "0",
pages = "S104--S113",
year = "2010",
DOI = "http://dx.doi.org/10.1016/j.diin.2010.05.013",
ISSN = "1742-2876",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "The Proceedings of the Tenth Annual {DFRWS}
Conference",
URL = "http://www.sciencedirect.com/science/article/pii/S174228761000040X",
abstract = "Hidden services are anonymously hosted services that
can be accessed over an anonymity network, such as Tor.
While most hidden services are legitimate, some host
illegal content. There has been a fair amount of
research on locating hidden services, but an open
problem is to develop a general method to prove that a
physical machine, once confiscated, was in fact the
machine that had been hosting the illegal content. In
this paper we assume that the hidden service logs
requests with some timestamp, and give experimental
results for leaving an identifiable fingerprint in this
log file as a timing channel that can be recovered from
the timestamps. In 60 min, we are able to leave a
36-bit fingerprint that can be reliably recovered. The
main challenges are the packet delays caused by the
anonymity network that requests are sent over and the
existing traffic in the log from the actual clients
accessing the service. We give data to characterize
these noise sources and then describe an implementation
of timing-channel fingerprinting for an Apache web
server based hidden service on the Tor network, where
the fingerprint is an additive channel that is
superencoded with a Reed Solomon code for reliable
recovery. Finally, we discuss the inherent tradeoffs
and possible approaches to making the fingerprint more
stealthy.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Fingerprints; Hidden services;
Timestamps; Timing channel; Tor network",
}
@InProceedings{Shengmin:2010:DSC,
author = "Z. Shengmin and W. Wenchao",
editor = "{IEEE}",
booktitle = "{2010 International Conference on Management and
Service Science (MASS), 24--26 Aug. 2010, Wuhan,
China}",
title = "Does [sic] {Chinese} Stock Indices Agree with
{Benford's Law}?",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--3",
year = "2010",
DOI = "http://dx.doi.org/10.1109/ICMSS.2010.5575999",
ISBN = "1-4244-5325-9, 1-4244-5326-7",
ISBN-13 = "978-1-4244-5325-2, 978-1-4244-5326-9",
LCCN = "????",
bibdate = "Mon Feb 18 18:12:46 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Book{Singleton:2010:FAF,
author = "Tommie Singleton and Aaron J. Singleton",
title = "Fraud auditing and forensic accounting",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Fourth",
pages = "xiv + 317",
year = "2010",
ISBN = "0-470-56413-X",
ISBN-13 = "978-0-470-56413-4",
LCCN = "HV8079.W47 B65 2010",
bibdate = "Tue Nov 22 10:31:33 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Wiley corporate F and A",
URL = "http://catalogimages.wiley.com/images/db/jimages/9780470564134.jpg;
http://catdir.loc.gov/catdir/enhancements/fy1007/2010013504-d.html;
http://catdir.loc.gov/catdir/enhancements/fy1007/2010013504-t.html;
http://catdir.loc.gov/catdir/enhancements/fy1011/2010013504-b.html",
abstract = "Completely revised and updated, Fraud Auditing and
Forensic Accounting, Fourth Edition reveals how to
develop an investigative eye toward both internal and
external fraud and provides crucial information on how
to deal with it when discovered. With new chapters on
the physiological aspects of the fraudster and on fraud
response, as well as new material on non-financial
aspects of fraud investigation, body language,
discourse analysis, and interviewing techniques, this
authoritative, timely book equips auditors,
investigators, corporate attorneys, and accountants to
identify the signs of financial fraud and successfully
investigate it",
acknowledgement = ack-nhfb,
remark = "Derived from third edition (2006). This book does not
discuss Benford's Law, but may be helpful background
for application of that law to the detection of
fraud.",
subject = "White collar crime investigation; United States;
Forensic accounting; Fraud investigation",
tableofcontents = "Background of Fraud Auditing and Forensic
Accounting \\
Fraud Principles \\
Fraud Schemes \\
Red Flags \\
Fraud Risk Assessment \\
Fraud Prevention \\
Fraud Detection \\
Fraud Response \\
Computer Crime \\
Fraud and the Accounting Information System \\
Gathering Evidence \\
Cyber Forensics \\
Obtaining and Evaluating Nonfinancial Evidence in a
Fraud Examination \\
General Criteria and Standards for Establishing an
Expert Witness's Qualifications \\
The Legal Role and Qualifications of an Expert Witness
\\
Effective Tactics and Procedures for the Expert Witness
in Court \\
Fraud and the Public Accounting Profession",
}
@Article{Stalcup:2010:BLH,
author = "Ken Stalcup",
title = "{Benford's Law}: How a Simple Misconception can Trip
up a Fraudster and How a Savvy {CFE} Can Spot It",
journal = "Fraud Magazine",
volume = "??",
number = "??",
pages = "??--??",
month = jan # "\slash " # feb,
year = "2010",
ISSN = "1553-6645",
ISSN-L = "1553-6645",
bibdate = "Sun Feb 17 07:57:24 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.fraud-magazine.com/article.aspx?id=203",
acknowledgement = ack-nhfb,
fjournal = "Fraud Magazine. {A} Publication of the Association of
Certified Fraud Examiners",
}
@Article{Strzalka:2010:SPB,
author = "Dominik Strza{\l}ka",
title = "On some properties of {Benford}'s law",
journal = "Journal of the {Korean Mathematical Society}",
volume = "47"