%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.10", %%% date = "04 July 2008", %%% time = "15:54:01 MDT", %%% filename = "marsaglia-george.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", %%% telephone = "+1 908 582 5828", %%% FAX = "1 908 582 7415", %%% checksum = "06622 3255 13888 142332", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "random numbers; statistics", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a bibliography of publications of %%% George Marsaglia, retired Professor of the %%% Department of Statistics, Florida State %%% University, Tallahassee, FL, USA. The %%% companion LaTeX file marsaglia-george.ltx can %%% be used to typeset this bibliography. %%% %%% In a trailing section, this bibliography also %%% contains publications that mention %%% Marsaglia's work in their titles. %%% %%% At version 1.10, the year coverage looked %%% like this: %%% %%% 1954 ( 1) 1972 ( 4) 1990 ( 5) %%% 1955 ( 0) 1973 ( 1) 1991 ( 2) %%% 1956 ( 0) 1974 ( 4) 1992 ( 2) %%% 1957 ( 2) 1975 ( 3) 1993 ( 6) %%% 1958 ( 0) 1976 ( 3) 1994 ( 2) %%% 1959 ( 0) 1977 ( 1) 1995 ( 2) %%% 1960 ( 0) 1978 ( 0) 1996 ( 1) %%% 1961 ( 2) 1979 ( 0) 1997 ( 3) %%% 1962 ( 0) 1980 ( 2) 1998 ( 3) %%% 1963 ( 2) 1981 ( 0) 1999 ( 1) %%% 1964 ( 8) 1982 ( 0) 2000 ( 4) %%% 1965 ( 4) 1983 ( 4) 2001 ( 1) %%% 1966 ( 1) 1984 ( 4) 2002 ( 2) %%% 1967 ( 3) 1985 ( 5) 2003 ( 4) %%% 1968 ( 2) 1986 ( 1) 2004 ( 5) %%% 1969 ( 2) 1987 ( 1) 2005 ( 3) %%% 1970 ( 2) 1988 ( 3) 2006 ( 1) %%% 1971 ( 1) 1989 ( 4) %%% %%% Article: 87 %%% Book: 3 %%% InCollection: 10 %%% InProceedings: 1 %%% Misc: 3 %%% Proceedings: 8 %%% TechReport: 5 %%% %%% Total entries: 117 %%% %%% This file is available as part of the BibNet %%% Project. The master copy is available for %%% public access on ftp.math.utah.edu in the %%% directory tree /pub/bibnet/authors. It is %%% mirrored to netlib.bell-labs.com in the %%% directory tree /netlib/bibnet/authors, from %%% which it is available via anonymous ftp and %%% the Netlib service. %%% %%% This bibliography was prepared from data in %%% the author's personal bibliography files, the %%% TeX User Group bibliography archive, the %%% BibNet Project bibliography archive, the %%% Karlsruhe Computer Science bibliography %%% archive, the University of Trier Digital %%% Bibliography and Library Project archives, %%% the MathSciNet database, the ACM Portal %%% database, the Compendex database, the IEEE %%% Xplore database, the Science Citation Index %%% database, and the ZentralBlatt Math database. %%% %%% 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{"\input path.sty"} %%% ==================================================================== %%% Institute abbreviations: @String{inst-MATHWORKS = "The MathWorks, Inc."} @String{inst-MATHWORKS:adr = "3 Apple Hill Drive, Natick, MA 01760-2098, USA"} %%% ==================================================================== %%% Journal abbreviations: @String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"} @String{j-ANN-APPL-PROBAB = "Annals of applied probability"} @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-ARS-COMB = "Ars Combinatoria. The Canadian Journal of Combinatorics"} @String{j-BIOMETRIKA = "Biometrika"} @String{j-CACM = "Communications of the ACM"} @String{j-CAN-MATH-BULL = "Canadian mathematical bulletin = Bulletin canadien de math{\'e}matiques"} @String{j-COMM-STAT-THEORY-METH = "Communications in Statistics. Theory and Methods"} @String{j-COMP-MATH-APPL = "Computers and Mathematics with Applications"} @String{j-COMP-MATH-APPL-B = "Computers and Mathematics with Applications. Part B"} @String{j-COMP-PHYS-COMM = "Computer Physics Communications"} @String{j-COMP-PHYSICS = "Computers in physics"} @String{j-CRYPTOLOGIA = "Cryptologia"} @String{j-IEEE-TRANS-COMPUT = "IEEE Transactions on Computers"} @String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"} @String{j-INFO-PROC-LETT = "Information Processing Letters"} @String{j-J-ACM = "Journal of the ACM"} @String{j-J-AM-STAT-ASSOC = "Journal of the American Statistical Association"} @String{j-J-FRANKLIN-INST = "Journal of the Franklin Institute"} @String{j-J-MOD-APPL-STAT-METH = "Journal of Modern Applied Statistical Methods"} @String{j-J-R-STAT-SOC-SER-B-METHODOL = "Journal of the Royal Statistical Society. Series B (Methodological)"} @String{j-J-STAT-COMPUT-SIMUL = "Journal of Statistical Computation and Simulation"} @String{j-J-STAT-SOFT = "Journal of Statistical Software"} @String{j-J-SUPERCOMPUTING = "The Journal of Supercomputing"} @String{j-LIN-MULT-ALGEBRA = "Linear and Multilinear Algebra"} @String{j-LINEAR-ALGEBRA-APPL = "Linear Algebra and its Applications"} @String{j-MANUSCR-MATH = "Manuscripta Mathematica"} @String{j-MATH-COMPUT = "Mathematics of Computation"} @String{j-METRIKA = "Metrika. International Journal for Theoretical and Applied Statistics."} @String{j-NUM-MATH = "Numerische Mathematik"} @String{j-PROC-AM-MATH-SOC = "Proceedings of the American Mathematical Society"} @String{j-PROC-NATL-ACAD-SCI-USA = "Proceedings of the National Academy of Sciences of the United States of America"} @String{j-SANKHYA-A = "Sankhy{\={a}} (Indian Journal of Statistics), Series A. Methods and Techniques"} @String{j-SIAM-J-SCI-STAT-COMP = "SIAM Journal on Scientific and Statistical Computing"} @String{j-SIAM-REVIEW = "SIAM Review"} @String{j-SIGADA-LETTERS = "ACM SIGADA Ada Letters"} @String{j-STAT-NEERLANDICA = "Statistica Neerlandica. Journal of the Netherlands Society for Statistics and Operations Research"} @String{j-STAT-PROB-LETT = "Statistics \& Probability Letters"} @String{j-TECHNOMETRICS = "Technometrics"} @String{j-TOMACS = "ACM Transactions on Modeling and Computer Simulation"} @String{j-TOMS = "ACM Transactions on Mathematical Software"} %%% ==================================================================== %%% Publishers and their addresses: @String{pub-ACADEMIC = "Academic Press"} @String{pub-ACADEMIC:adr = "New York, NY, USA"} @String{pub-AMS = "American Mathematical Society"} @String{pub-AMS:adr = "Providence, RI, USA"} @String{pub-ELS = "Elsevier Science Publishers B.V."} @String{pub-ELS:adr = "Amsterdam, The Netherlands"} @String{pub-SV = "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr = "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-VAN-NOSTRAND-REINHOLD = "Van Nostrand Reinhold"} @String{pub-VAN-NOSTRAND-REINHOLD:adr = "New York, NY, USA"} %%% ==================================================================== %%% Bibliography entries, sort by year and citation label: @Article{Marsaglia:1954:ILC, author = "George Marsaglia", title = "Iterated limits and the central limit theorem for dependent variables", journal = j-PROC-AM-MATH-SOC, volume = "5", pages = "987--991", year = "1954", CODEN = "PAMYAR", ISSN = "0002-9939", MRclass = "60.0X", MRnumber = "16,494e", MRreviewer = "D. G. Kendall", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database; ZentralBlatt Math database", keywords = "Probability theory", ZMnumber = "0056.36102", } @Article{Graybill:1957:IMQ, author = "Franklin A. Graybill and George Marsaglia", title = "Idempotent matrices and quadratic forms in the general linear hypothesis", journal = j-ANN-MATH-STAT, volume = "28", pages = "678--686", year = "1957", CODEN = "AASTAD", ISSN = "0003-4851", MRclass = "62.0X", MRnumber = "19,1095e", MRreviewer = "M. Dwass", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", keywords = "Statistics", ZMnumber = "0080.35502", ZMreviewer = "T. V. Narayana", } @Article{Marsaglia:1957:NCM, author = "George Marsaglia", title = "A note on the construction of a multivariate normal sample", journal = j-IEEE-TRANS-INF-THEORY, volume = "3", number = "2", pages = "149--149", month = jun, year = "1957", CODEN = "IETTAW", ISSN = "0018-9448", bibdate = "Thu Aug 05 08:58:22 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://ieeexplore.ieee.org/", abstract = "This note points out the superfluity of a method of Stein and Storer for constructing a multivariate normal sample, and suggests a simple alternative.", acknowledgement = ack-nhfb, } @Article{Marsaglia:1961:ERV, author = "G. Marsaglia", title = "Expressing a random variable in terms of uniform random variables", journal = j-ANN-MATH-STAT, volume = "32", number = "3", pages = "894--898", year = "1961", CODEN = "AASTAD", ISSN = "0003-4851", MRclass = "65.15", MRnumber = "23 \#B3122", MRreviewer = "M. E. Muller", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", keywords = "probability theory", ZMnumber = "0139.35604", } @Article{Marsaglia:1961:GER, author = "G. Marsaglia", title = "Generating exponential random variables", journal = j-ANN-MATH-STAT, volume = "32", pages = "899--900", year = "1961", CODEN = "AASTAD", ISSN = "0003-4851", MRclass = "65.15", MRnumber = "23 \#B3123", MRreviewer = "M. E. Muller", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", keywords = "probability theory", ZMnumber = "0139.35603", } @Article{Marsaglia:1963:END, author = "George Marsaglia", title = "Expressing the normal distribution with covariance matrix ${A}+{B}$ in terms of one with covariance matrix ${A}$", journal = j-BIOMETRIKA, volume = "50", pages = "535--538", year = "1963", CODEN = "BIOKAX", ISSN = "0006-3444", MRclass = "62.40", MRnumber = "31 \#5290", MRreviewer = "I. Olkin", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", keywords = "statistics", ZMnumber = "0117.37202", } @Article{Marsaglia:1963:GDR, author = "G. Marsaglia", title = "Generating discrete random variables in a computer", journal = j-CACM, volume = "6", number = "1", pages = "37--38", month = jan, year = "1963", CODEN = "CACMA2", ISSN = "0001-0782", bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", country = "USA", date = "13/05/93", descriptors = "RVG;", enum = "7628", keywords = "numerical analysis", location = "SEL: Wi", references = "0", revision = "16/01/94", ZMnumber = "0112.08402", } @Article{MacLaren:1964:FPG, author = "M. D. MacLaren and G. Marsaglia and T. A. Bray", title = "A fast procedure for generating exponential random variables", journal = j-CACM, volume = "7", number = "5", pages = "298--300", month = may, year = "1964", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Fri Nov 25 18:19:53 MST 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib; ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", country = "USA", date = "13/05/93", descriptors = "RVG;", enum = "7614", keywords = "numerical analysis; PRNG (pseudo-random number generator)", location = "SEL: Wi", references = "0", revision = "16/01/94", ZMnumber = "0127.09101", } @Article{Marsaglia1964c, author = "G. Marsaglia and M. D. MacLaren and T. A. Bray", title = "A fast procedure for generating normal random variables", journal = j-CACM, volume = "7", number = "1", pages = "4--10", month = jan, year = "1964", CODEN = "CACMA2", ISSN = "0001-0782", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib; ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", country = "USA", date = "13/05/93", descriptors = "RVG;", enum = "7637", location = "SEL: Wi", references = "0", revision = "16/01/94", } @Article{Marsaglia:1964:CMC, author = "G. Marsaglia", title = "Conditional means and covariances of normal variables with singular covariance matrix", journal = j-J-AM-STAT-ASSOC, volume = "59", pages = "1203--1204", year = "1964", CODEN = "JSTNAL", ISSN = "0162-1459", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", keywords = "statistics", ZMnumber = "0124.11303", } @Article{Marsaglia:1964:CMG, author = "G. Marsaglia and T. A. Bray", title = "A convenient method for generating normal variables", journal = j-SIAM-REVIEW, volume = "6", number = "3", pages = "260--264", year = "1964", CODEN = "SIREAD", ISSN = "0036-1445 (print), 1095-7200 (electronic)", MRclass = "65.15", MRnumber = "30 \#2660", MRreviewer = "D. H. Lehmer", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", keywords = "numerical analysis", ZMnumber = "0125.08001", } @Article{Marsaglia:1964:FPG, author = "G. Marsaglia and M. D. MacLaren and T. A. Bray", title = "A fast procedure for generating normal random variables", journal = j-CACM, volume = "7", number = "1", pages = "4--10", month = jan, year = "1964", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Fri Nov 25 18:19:51 MST 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib; ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://portal.acm.org/; http://www.acm.org/pubs/contents/journals/cacm/", acknowledgement = ack-nhfb, country = "USA", descriptors = "RVG;", enum = "7637", keywords = "numerical analysis; PRNG (pseudo-random number generator)", language = "English", location = "SEL: Wi", references = "0", revision = "16/01/94", ZMnumber = "0127.09005", } @Article{Marsaglia:1964:GVT, author = "G. Marsaglia", title = "Generating a variable from the tail of the normal distribution", journal = j-TECHNOMETRICS, volume = "6", number = "1", pages = "101--102", year = "1964", CODEN = "TCMTA2", ISSN = "0040-1706", bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", date = "13/05/93", descriptors = "RVG;", enum = "7629", location = "SEL: Wi", references = "0", revision = "16/01/94", } @InCollection{Marsaglia:1964:RVC, author = "George Marsaglia", title = "Random variables and computers", crossref = "Kozesnik:1964:TTP", pages = "499--512", year = "1964", MRclass = "65.05 (65.15)", MRnumber = "29 \#1721", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", keywords = "probability theory", ZMnumber = "0123.36205", } @Article{MacLaren:1965:URN, author = "M. Donald MacLaren and George Marsaglia", title = "Uniform Random Number Generators", journal = j-J-ACM, volume = "12", number = "1", pages = "83--89", month = jan, year = "1965", CODEN = "JACOAH", ISSN = "0004-5411", MRclass = "65.15", MRnumber = "30 \#687", bibdate = "Mon Jan 22 17:05:44 MST 2001", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/jacm.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", acknowledgement = ack-nhfb, keywords = "numerical analysis", oldlabel = "MacLarenM65", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/jacm/MacLarenM65", ZMnumber = "0143.40101", } @Article{Marsaglia:1965:CER, author = "G. Marsaglia", title = "The cumulative effect of random losses in a transmission line", journal = j-J-FRANKLIN-INST, volume = "280", pages = "443--450", year = "1965", ISSN = "0016-0032", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", keywords = "information, communication", ZMnumber = "0173.21401", } @Article{Marsaglia:1965:MCR, author = "G. Marsaglia and A. W. Marshall and F. Proschan", title = "Moment crossings as related to density crossings", journal = j-J-R-STAT-SOC-SER-B-METHODOL, volume = "27", pages = "91--93", year = "1965", CODEN = "JSTBAJ", ISSN = "0035-9246", MRclass = "60.20", MRnumber = "32 \#6514", MRreviewer = "D. R. Barr", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", keywords = "statistics", ZMnumber = "0128.38905", } @Article{Marsaglia:1965:RNV, author = "George Marsaglia", title = "Ratios of normal variables and ratios of sums of uniform variables", journal = j-J-AM-STAT-ASSOC, volume = "60", pages = "193--204", year = "1965", CODEN = "JSTNAL", ISSN = "0162-1459", MRclass = "60.20", MRnumber = "31 \#2747", MRreviewer = "S. R. Searle", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", keywords = "statistics", ZMnumber = "0126.35302", } @Article{Marsaglia1966, author = "G. Marsaglia", title = "A general method for producing random variables in a computer", journal = "Proc. of the Fall Joint Computer Conf., San Francisco, Nov.", pages = "169--173", year = "1966", bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", country = "USA", date = "13/05/93", descriptors = "RVG;", enum = "7631", location = "SEL: Wi", references = "0", revision = "16/01/94", town = "San Francisco", } @InCollection{Marsaglia:1967:BRS, author = "George Marsaglia", title = "Bounds on the rank of the sum of matrices", crossref = "Kozesnik:1967:TFP", pages = "455--462", year = "1967", MRclass = "15.05", MRnumber = "36 \#1458", MRreviewer = "C. G. Cullen", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", } @Article{Marsaglia:1968:OLR, author = "George Marsaglia and T. A. Bray", title = "One-line random number generators and their use in combinations", journal = j-CACM, volume = "11", number = "11", pages = "757--759", month = nov, year = "1968", CODEN = "CACMA2", ISSN = "0001-0782", MRclass = "65.15", MRnumber = "39\#5040", MRreviewer = "R. R. Coveyou", bibdate = "Fri Nov 25 18:20:22 MST 2005", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", abstract = "Some one-line random number generators, i.e. generators requiring a single FORTRAN instruction are discussed, and some short FORTRAN programs which mix several such generators are described. The aim is to provide methods for incorporating random number generators directly in FORTRAN programs, by means of a few in-line instructions. The advantages are speed (avoiding linkage to and from a subroutine), convenience, and versatility. Anyone wishing to experiment with generators, either using congruential generators by themselves or mixing several generators to provide a composite with potentially better statistical properties than the library generators currently available, may wish to consider some of the simple FORTRAN program discussed here.", acknowledgement = ack-nhfb, classcodes = "C6150E (General utility programs)", corpsource = "Boeing Scientific Research Lab., Seattle, WA, USA", keywords = "FORTRAN; Monte Carlo; numerical analysis; PRNG (pseudo-random number generator); random number generation; simulation; utility programs", ZMnumber = "0164.18802", ZMreviewer = "R. R. Coveyou", } @Article{Marsaglia:1968:RNF, author = "George Marsaglia", title = "Random numbers fall mainly in the planes", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "61", number = "1", pages = "25--28", day = "15", month = sep, year = "1968", CODEN = "PNASA6", ISSN = "0027-8424", MRclass = "65.15", MRnumber = "38 \#3998", MRreviewer = "R. R. Coveyou", bibdate = "Thu Nov 14 11:39:48 2002", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", note = "A popularized account of this work appeared as ``Are random numbers really random?'' [Scientific Research (Philadelphia, PA), 3 (1968), 21--??]. This widely-cited paper describes the hyperplane problem that linear congruential generators suffer from, although careful choice of multipliers can minimize its importance: see \cite{Coveyou:1967:FAU,Dyadkin:1997:SBM,Dyadkin:1997:FEL,Dyadkin:2000:SBM}.", acknowledgement = ack-nhfb, keywords = "numerical analysis; PRNG (pseudo-random number generator)", ZMnumber = "0172.21002", } @Article{Whittlesey:1969:LEM, author = "John R. B. Whittlesey", title = "Letter to the {Editor}: {On} the Multidimensional Uniformity of Pseudorandom Generators", journal = j-CACM, volume = "12", number = "5", pages = "247--247", month = may, year = "1969", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Fri Nov 25 18:20:26 MST 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://www.acm.org/pubs/contents/journals/cacm/", note = "See \cite{Marsaglia:1968:RNF}.", acknowledgement = ack-nhfb, annote = "It would appear that George Marsaglia's recent article proving that all the pseudorandom points generated in the unit n-cube ``will be found to lie in a relatively small number of parallel hyperplanes'' has given the coup de grace, to the use of multiplicative congruential generators in all Monte Carlo applications, except those having the most non-stringent requirements for multidimensional uniformity.", country = "USA", descriptors = "Comparison; shift register sequences; Tausworthe generator; RNG; test; multidimensional uniformity; grid structure; linear congruential generator;", enum = "3286", keywords = "PRNG (pseudo-random number generator)", references = "7", } @InCollection{Marsaglia:1970:OSA, author = "G. Marsaglia", title = "One-sided approximations by linear combinations of functions", crossref = "Talbot:1969:ATP", pages = "233--242", year = "1970", MRclass = "65.30", MRnumber = "42 \#1307", MRreviewer = "G. Opfer", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", ZMclass = "*90-04 Machine computation, programs (optimization) 90C05 Linear programming 41A50 Best approximation", ZMnumber = "0246.90027", } @Article{Marsaglia:1970:RCR, author = "George Marsaglia", title = "Regularities in congruential random number generators", journal = j-NUM-MATH, volume = "16", number = "1", pages = "8--10", year = "1970", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", MRclass = "65.15", MRnumber = "42 \#8651", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/nummath.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", acknowledgement = ack-nhfb, classification = "C7890 (Other special applications of computing)", corpsource = "Boeing Sci. Res. Labs., Seattle, WA, USA", keywords = "random number generation", xxyear = "1970/1971", ZMclass = "*65C10 Random number generation", ZMnumber = "0212.18204", } @Article{Marsaglia:1971:RVI, author = "George Marsaglia", title = "Random variables with independent binary digits", journal = j-ANN-MATH-STAT, volume = "42", pages = "1922--1929", year = "1971", CODEN = "AASTAD", ISSN = "0003-4851", MRclass = "60A05", MRnumber = "45 \#7764", MRreviewer = "A. Fuchs", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", ZMclass = "*60E05 General theory of probability distributions 60F99 Limit theorems (probability)", ZMnumber = "0239.60015", } @Article{Marsaglia:1972:CPS, author = "George Marsaglia", title = "Choosing a point from the surface of a sphere", journal = j-ANN-MATH-STAT, volume = "43", pages = "645--646", year = "1972", CODEN = "AASTAD", ISSN = "0003-4851", MRclass = "65C10", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", ZMclass = "*65C10 Random number generation", ZMnumber = "0248.65008", } @InCollection{Marsaglia:1972:SLC, author = "George Marsaglia", title = "The Structure of Linear Congruential Sequences", crossref = "Zaremba:1972:ANT", pages = "249--285", year = "1972", MRclass = "65C05", MRnumber = "53 \#14854", MRreviewer = "J. H. Halton", bibdate = "Mon Aug 02 10:41:44 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", acknowledgement = ack-nhfb, ZMclass = "*65C10 Random number generation", ZMnumber = "0266.65007", } @Article{Marsaglia:1972:WD, author = "G. Marsaglia and G. P. H. Styan", title = "When does {${\rm rank}\ (A+B)={\rm rank}(A)+{\rm rank}(B)$}?", journal = j-CAN-MATH-BULL, volume = "15", pages = "451--452", year = "1972", CODEN = "CMBUA3", ISSN = "0008-4395", MRclass = "15A03", MRnumber = "47 \#236", MRreviewer = "A. R. Amir-Moez", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", ZMclass = "*15A03 Vector spaces", ZMnumber = "0252.15002", } @TechReport{Marsaglia:1973:HUM, author = "George Marsaglia and K. Ananthanarayanan and A. Zaman", title = "How to use the {McGill} random-number package {SUPER-DUPER}", type = "Technical report", institution = "School of Computer Science, McGill University", address = "Montreal, Quebec, Canada", year = "1973", bibdate = "Thu Dec 20 20:19:47 2007", acknowledgement = ack-nhfb, } @Article{Marsaglia:1974:APR, author = "George Marsaglia", title = "Acknowledgement of priority to: ``{Random} variables with independent binary digits'' {(Ann. Math. Statist. {\bf 42} (1971), 1922--1929)}", journal = j-ANN-STAT, volume = "2", pages = "848", year = "1974", CODEN = "ASTSC7", ISSN = "0090-5364", MRclass = "60A10", MRnumber = "50 \#1310", MRreviewer = "A. Fuchs", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", ZMclass = "*60E05 General theory of probability distributions 60F99 Limit theorems (probability)", ZMnumber = "0284.60017", } @Article{Marsaglia:1974:APRb, author = "George Marsaglia", title = "Acknowledgement of priority to: ``{Random} variables with independent binary digits'' {(Ann. Math. Statist. {\bf 42} (1971), 1922--1929)}", journal = j-ANN-PROBAB, volume = "2", pages = "747", year = "1974", CODEN = "APBYAE", ISSN = "0091-1798", MRclass = "60A05", MRnumber = "49 \#8070", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", ZMclass = "*60E05 General theory of probability distributions 60F99 Limit theorems (probability)", ZMnumber = "0284.60018", } @Article{Marsaglia:1974:EIR, author = "George Marsaglia and George P. H. Styan", title = "Equalities and inequalities for ranks of matrices", journal = j-LIN-MULT-ALGEBRA, volume = "2", pages = "269--292", year = "1974/75", CODEN = "LNMLAZ", ISSN = "0308-1087", MRclass = "15A45", MRnumber = "52 \#5711", MRreviewer = "A. R. Amir-Moez", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", ZMclass = "*15A03 Vector spaces 15A39 Linear inequalities 15A45 Miscellaneous inequalities involving matrices", ZMnumber = "0297.15003", } @Article{Marsaglia:1974:RCG, author = "George Marsaglia and George P. H. Styan", title = "Rank conditions for generalized inverses of partitioned matrices", journal = j-SANKHYA-A, volume = "36", number = "4", pages = "437--442", year = "1974", CODEN = "SANABS", ISSN = "0036-4452", MRclass = "15A09", MRnumber = "52 \#5699", MRreviewer = "Thomas L. Boullion", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", ZMclass = "*15A09 Matrix inversion 15A03 Vector spaces", ZMnumber = "0309.15002", } @InCollection{Marsaglia:1975:EAL, author = "G. Marsaglia", title = "Extension and applications of {Lukacs}' characterization of the gamma distribution", crossref = "Saleh:1975:PSS", pages = "13", year = "1975", MRclass = "62E10", MRnumber = "55 \#6633", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", remark = "Paper number 9.", } @Article{Marsaglia:1975:NLM, author = "George Marsaglia and Alberto Tubilla", title = "A note on the ``lack of memory'' property of the exponential distribution", journal = j-ANN-PROBAB, volume = "3", pages = "353--354", year = "1975", CODEN = "APBYAE", ISSN = "0091-1798", MRclass = "62E10", MRnumber = "51 \#2073", MRreviewer = "Ramesh C. Gupta", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", ZMclass = "*60E05 General theory of probability distributions 62E10 Structure theory of statistical distributions", ZMnumber = "0336.60017", } @Article{Marsaglia:1976:IFM, author = "G. Marsaglia and K. Ananthanarayanan and N. J. Paul", title = "Improvements on fast methods for generating normal random variables", journal = j-INFO-PROC-LETT, volume = "5", number = "2", pages = "27--30", month = jun, year = "1976", CODEN = "IFPLAT", ISSN = "0020-0190", MRclass = "65C10", MRnumber = "55 \#11560", MRreviewer = "I. Vaduva", bibsource = "Compendex database; ftp://ftp.math.utah.edu/pub/tex/bib/infoproc1970.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://dblp.uni-trier.de/db/journals/ipl/ipl5.html#MarsagliaAP76; MathSciNet database", acknowledgement = ack-nhfb, classification = "922; B0240G (Monte Carlo methods); C1140G (Monte Carlo methods); C7890 (Other special applications of computing)", corpsource = "School of Computer Sci., McGill Univ., Montreal, Que., Canada", journalabr = "Inf Process Lett", keywords = "mathematical programming; mathematical statistics; Monte Carlo; Monte Carlo methods; normal random variables; random number generation; random numbers; rectangle tooth tail method; simulation", oldlabel = "MarsagliaAP76", treatment = "A Application; T Theoretical or Mathematical", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/ipl/MarsagliaAP76", ZMclass = "*65C10 Random number generation 65C05 Monte Carlo methods", ZMnumber = "0332.65003", } @InCollection{Marsaglia:1976:RNG, author = "George Marsaglia", title = "Random number generation", crossref = "Ralston:1976:ECS", pages = "1192--1197", year = "1976", bibdate = "Mon Aug 02 16:34:17 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, } @Article{Marsaglia:1977:SMG, author = "George Marsaglia", title = "The squeeze method for generating gamma variates", journal = j-COMP-MATH-APPL, volume = "3", number = "4", pages = "321--325", year = "1977", CODEN = "CMAPDK", ISSN = "0097-4943, 0898-1221", MRclass = "65C10", MRnumber = "58 \#13613", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", ZMclass = "*65C10 Random number generation 60E05 General theory of probability distributions", ZMnumber = "0384.65005", } @Article{Marsaglia:1980:GNS, author = "George Marsaglia", title = "Generating a Normal Sample with Given Sample Mean and Variance", journal = j-J-STAT-COMPUT-SIMUL, volume = "11", number = "1", pages = "71--73", month = "????", year = "1980", CODEN = "JSCSAJ", ISSN = "0094-9655", bibdate = "Thu Aug 05 09:10:47 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://jscs.stat.vt.edu/JSCS/articles/v11n1.html; Science Citation Index", acknowledgement = ack-nhfb, } @Article{Marsaglia:1980:GRV, author = "George Marsaglia", title = "Generating random variables with a $t$-distribution", journal = j-MATH-COMPUT, volume = "34", number = "149", pages = "235--236", month = jan, year = "1980", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65C10", MRnumber = "81a:65015", bibsource = "Distributed/QLD.bib; Distributed/QLD/1980.bib; ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1980.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; JSTOR database; MathSciNet database", fjournal = "Mathematics of Computation", keywords = "algorithm; t-distribution", ZMclass = "*65C10 Random number generation 65C05 Monte Carlo methods", ZMnumber = "0423.65005", } @InCollection{Marsaglia:1983:RNG, author = "George Marsaglia", title = "Random number generation", crossref = "Ralston:1983:ECS", pages = "1260--1264", year = "1983", bibdate = "Mon Aug 02 10:57:24 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, xxnote = "Text virtually identical with first edition \cite{Marsaglia:1976:RNG}. See also third edition \cite{Marsaglia:1993:RNG}.", } @Article{Marsaglia:1983:RVI, author = "George Marsaglia", title = "Random variables with independent binary digits", journal = "Kibern. Sb., Nov. Ser.", volume = "20", pages = "216--224", year = "1983", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", abstract = "Translation from Ann. Math. Stat. 42, 1922--1929 (1971; Zbl 0239.60015).", keywords = "independent binary digits", language = "Russian", ZMclass = "*60E05 General theory of probability distributions 60F99 Limit theorems (probability)", ZMnumber = "0535.60013", } @Article{Marsaglia:1984:EAM, author = "George Marsaglia", title = "The exact-approximation method for generating random variables in a computer", journal = j-J-AM-STAT-ASSOC, volume = "79", number = "385", pages = "218--221", year = "1984", CODEN = "JSTNAL", ISSN = "0162-1459", MRclass = "65C10", MRnumber = "85d:65010", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", abstract = "A suitably chosen approximation to the inverse of a probability distribution can lead to exact and very fast methods for generating random variables, if the approximation is made exact by adjusting the argument of the approximating function. This article describes the basic method and extensions of it. It gives four examples, of which two are methods for generating gamma-and t-variates that, while meant to illustrate the basic method, show promise of being faster than the best current methods.", fjournal = "Journal of the American Statistical Association", keywords = "gamma-and t-variates; inverse of a probability distribution", ZMclass = "*65C10 Random number generation 65C05 Monte Carlo methods", ZMnumber = "0552.65005", } @Article{Marsaglia:1984:FEI, author = "George Marsaglia and Wai Wan Tsang", title = "A fast, easily implemented method for sampling from decreasing or symmetric unimodal density functions", journal = j-SIAM-J-SCI-STAT-COMP, volume = "5", number = "2", pages = "349--359", month = jun, year = "1984", CODEN = "SIJCD4", ISSN = "0196-5204", MRclass = "65U05 (65C10)", MRnumber = "86a:65137", MRreviewer = "Mervin Muller", bibdate = "Tue Apr 29 19:18:28 MDT 1997", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/fortran2.bib; ftp://ftp.math.utah.edu/pub/tex/bib/matlab.bib; ftp://ftp.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", abstract = "From authors' summary: The fastest computer methods for sampling from a given density are those based on a mixture of a fast and a slow part. This paper describes a new method of this type, suitable for any decreasing or symmetric unimodal density. It differs from others in that it is faster and more easily implemented. It is called the ziggurat method, after the shape of a single, convenient density that provides for both the fast and slow part of the generating process. Examples are given for REXP and RNOR subroutines that generate exponential and normal variates that, as assembler routines, are nearly twice as fast as the previous assembler routines, and that as Fortran routines, approach the limiting possible speed appropriately defined.", acknowledgement = ack-nhfb, annote = "An updated version of this algorithm (see \cite{Marsaglia:2000:ZMG}) is used in Matlab's randn() function for generating normally-distributed pseudo-random numbers; see \cite{Moler:2001:CCN}.", classification = "B0240G (Monte Carlo methods); C1140G (Monte Carlo methods); C7310 (Mathematics computing)", corpsource = "Computer Sci. Dept., Washington State Univ., Pullman, WA, USA", fjournal = "Society for Industrial and Applied Mathematics. Journal on Scientific and Statistical Computing", keywords = "exponential random variables; FORTRAN subroutine; Fortran subroutines; Monte Carlo; Monte Carlo methods; normal random variables; numerical analysis; random numbers; REXP; RNOR; sampling; simulation; subroutines; symmetric unimodal density functions; ziggurat method", treatment = "N New Development; P Practical; T Theoretical or Mathematical", ZMclass = "*65C99 Numerical simulation 65C10 Random number generation 62D05 Statistical sampling theory", ZMnumber = "0573.65116", ZMreviewer = "L. Bondesson", } @Article{Marsaglia:1984:GCM, author = "George Marsaglia and Ingram Olkin", title = "Generating correlation matrices", journal = j-SIAM-J-SCI-STAT-COMP, volume = "5", number = "2", pages = "470--475", year = "1984", CODEN = "SIJCD4", ISSN = "0196-5204", MRclass = "65C10 (62H99)", MRnumber = "85h:65018", MRreviewer = "G. P. Bhattacharjee", bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; ftp://ftp.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", abstract = "This paper describes a variety of methods for generating random correlation matrices, with emphasis on choice of random variables and distributions so as to provide matrices with given structure, expected values of eigenvalues.", acknowledgement = ack-nhfb, classification = "B0240G (Monte Carlo methods); C1140G (Monte Carlo methods)", corpsource = "Computer Sci. Dept., Washington State Univ., Pullmann, WA, USA", fjournal = "Society for Industrial and Applied Mathematics. Journal on Scientific and Statistical Computing", keywords = "correlation matrices generation; eigenvalues; eigenvalues and eigenfunctions; matrix algebra; Monte Carlo methods; random correlation matrices; random variables", treatment = "T Theoretical or Mathematical", ZMclass = "*65C10 Random number generation 65F30 Other matrix algorithms 62J05 Linear regression", ZMnumber = "0552.65006", } @InProceedings{Marsaglia:1985:CVR, author = "George Marsaglia", title = "A Current View of Random Number Generators", crossref = "Billard:1985:CSS", pages = "3--10", year = "1985", bibdate = "Thu Dec 18 13:39:28 2003", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", URL = "http://stat.fsu.edu/pub/diehard/; http://www.evensen.org/marsaglia/keynote.ps", acknowledgement = ack-nhfb, } @Article{Marsaglia:1985:MSR, author = "George Marsaglia and Liang-Huei Tsay", title = "Matrices and the structure of random number sequences", journal = j-LINEAR-ALGEBRA-APPL, volume = "67", pages = "147--156", year = "1985", CODEN = "LAAPAW", ISSN = "0024-3795", MRclass = "65C10 (15A99)", MRnumber = "86g:65018", MRreviewer = "Gheorghe Barbu", bibdate = "Thu Jan 23 11:18:08 MST 1997", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", abstract = "This paper discusses the maximum period and randomness structure of two random number generators: shift-register and lagged-Fibonacci. Two theorems on the period of the random number generators are derived using linear algebra and matrix theory. Some regularities of m-tuples of points are shown for the shift-register generators analogous to that for the congruential random number generators. It is also suggested that no such regularities are appeared for the lagged-Fibonacci generators since lags are long enough.", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", keywords = "lagged Fibonacci; maximal period; randomness; shift-register", ZMclass = "*65C10 Random number generation", ZMnumber = "0572.65002", ZMreviewer = "K. Uosaki", } @Article{Marsaglia:1985:NPT, author = "George Marsaglia", title = "Note on a proposed test for random number generators", journal = j-IEEE-TRANS-COMPUT, volume = "34", number = "8", pages = "756--758", year = "1985", CODEN = "ITCOB4", ISSN = "0018-9340", MRclass = "65C10", MRnumber = "86h:65010", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://dblp.uni-trier.de/db/journals/tc/tc34.html#Marsaglia85; MathSciNet database", abstract = "This paper shows that many random number generators with symmetric output would have the same mean as a truly uniform random number generator in the recently proposed test by {\it J. Savir} [IEEE Trans. Comput. C-32, 960--961 (1983; Zbl 0518.65003)] and pass the test. So, the author provides a better test based on the exact distribution of the outcome of random number sequences. The distribution is derived by using Markov chain model.", fjournal = "Institute of Electrical and Electronics Engineers. Transactions on Computers", keywords = "Markov chain; test of randomness; uniform random number", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/tc/Marsaglia85", ZMclass = "*65C10 Random number generation", ZMnumber = "0572.65001", ZMreviewer = "K. Uosaki", } @Article{Marsaglia:1986:IFC, author = "George Marsaglia", title = "The incomplete ${\Gamma}$ function as a continuous Poisson distribution", journal = j-COMP-MATH-APPL-B, volume = "12", pages = "1187--1190", year = "1986", CODEN = "CMAPDK", ISSN = "0097-4943, 0898-1221", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", abstract = "The paper illustrates the use of the incomplete $\Gamma$ function as a means for computer generation of Poisson random variables.", keywords = "computer generation of Poisson random variables; incomplete gamma function", ZMclass = "*65C99 Numerical simulation 65C10 Random number generation 62E99 Statistical distribution theory 65D20 Computation of special functions", ZMnumber = "0628.65149", ZMreviewer = "P. Reichensperger", } @Article{Tsang:1987:DTA, author = "Wai Wan Tsang and George Marsaglia", title = "A decision tree algorithm for squaring histograms in random number generation", journal = j-ARS-COMB, volume = "23A", pages = "291--301", year = "1987", CODEN = "????", ISSN = "0381-7032", MRclass = "65C10", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", abstract = "The squaring histogram method is a fast and flexible way for generating random variables. It was developed by the second author based upon the alias method suggested by A. J. Walker. This paper describes a new algorithm for the set-up procedure of the squaring histogram method. The algorithm organizes data into a binary search tree so that insertion of elements and searching for minimum and maximum can be done in O(log n) time. The average time complexity of the algorithm is O(n log n) while the worst-case complexity is $O(n^2)$. Empirical results confirm that the algorithm runs much faster than the previously fastest algorithm whose time complexity is $O(n^2)$. Moreover, the proposed algorithm can be implemented on a computer without using more data storage than the existing algorithms.", keywords = "algorithms; average time complexity; random number generation; squaring histogram method; worst-case complexity", ZMclass = "*65C10 Random number generation", ZMnumber = "0614.65002", } @Article{Marsaglia:1989:AAU, author = "George Marsaglia and Arif Zaman and Y. L. Zheng", title = "An Algorithm for the Area of the Union of a Collection of Convex Sets", journal = j-J-STAT-COMPUT-SIMUL, volume = "31", number = "1", pages = "46--49", month = "????", year = "1989", CODEN = "JSCSAJ", ISSN = "0094-9655", bibdate = "Thu Aug 05 09:22:20 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://jscs.stat.vt.edu/JSCS/articles/v31n1.html; http://web.lums.edu.pk/~arifz/resume.html", acknowledgement = ack-nhfb, xxnote = "Check author order??", } @InCollection{Marsaglia:1989:CGD, author = "George Marsaglia", title = "The {$X+Y,\; X/Y$} characterization of the gamma distribution", crossref = "Gleser:1989:CPS", pages = "91--98", year = "1989", MRclass = "60E10 (62E10)", MRnumber = "91a:60049", MRreviewer = "Moshe Shaked", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", } @Article{Marsaglia:1989:NSS, author = "George Marsaglia and Arif Zaman and John C. W. Marsaglia", title = "Numerical solution of some classical differential-difference equations", journal = j-MATH-COMPUT, volume = "53", number = "187", pages = "191--201", month = jul, year = "1989", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65L05 (65Q05)", MRnumber = "90h:65124", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1980.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; JSTOR database; MathSciNet database", abstract = "This article describes a method for evaluating of Renyi's, Dickman's and Buchstab's functions with defining relations, respectively: $[(x- 1)f(x)]'=2f(x-1),$ $XV'(x)=-V(x-1)$ and $[XW(x)]'=W(x-1),$ respectively. The method gives numerical solutions accurate to hundreds or even thousands of digits.", acknowledgement = ack-nhfb, classcodes = "C4170 (Differential equations); C1120 (Analysis)", corpsource = "Dept. of Stat., Florida State Univ., Tallahassee, FL, USA", fjournal = "Mathematics of Computation", keywords = "Buchstab's function; classical differential-difference equations; classical problems; Dickman's function; difference equations; differential equations; differential-difference equations; numerical; Renyi's function; solutions", treatment = "T Theoretical or Mathematical", ZMclass = "*65L05 Initial value problems for ODE (numerical methods) 65D20 Computation of special functions 34K05 General theory of functional-differential equations", ZMnumber = "0675.65073", ZMreviewer = "P. I. Ialamov", } @Article{Marsaglia:1990:DBR, author = "George Marsaglia and B. Narasimhan and Arif Zaman", title = "The distance between random points in rectangles", journal = j-COMM-STAT-THEORY-METH, volume = "19", number = "11", pages = "4199--4212", year = "1990", CODEN = "CSTMDC", ISSN = "0361-0926", MRclass = "60D05 (62E15)", MRnumber = "92b:60015", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", abstract = "Consider two oriented rectangles in ${\bbfR}^2$ with sides parallel to the x and y axes, possibly overlapping or even coincident; choose a point randomly and uniformly in each rectangle. This paper describes a method for finding the distribution function for the random distance between the points. The required density is described as a sum of elementary integrals whose computation is then reduced to evaluations of one particular function. For this a Fortran program is described. Several special cases are treated more specifically.", fjournal = "Communications in Statistics. Theory and Methods", keywords = "Fortran program; random distance between the points", ZMclass = "*60D05 Geometric probability 60-04 Machine computation, programs (probability theory)", ZMnumber = "0731.60012", ZMreviewer = "W. J. Firey (Corvallis)", } @Article{Marsaglia:1990:NDS, author = "George Marsaglia and John C. W. Marsaglia", title = "A new derivation of {Stirling}'s approximation to {$n!$}", journal = j-AMER-MATH-MONTHLY, volume = "97", number = "9", pages = "826--829", month = nov, year = "1990", CODEN = "AMMYAE", ISSN = "0002-9890", MRclass = "41A60 (01A50 05A10)", MRnumber = "92b:41049", MRreviewer = "E. Rodney Canfield", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", abstract = "A derivation of Stirling's formula $n! \sim n^ne^{-n} \sqrt {2 \pi n^n}$ is presented. To this purpose the authors consider the relation $n!=\int^\infty_0x^ne^{-x}dx$. Their proof is not new; see {\it Nathaniel Grossman} [Letter to the editor, Am. Math. Mon. 98, No. 3, 233 (1991)].", fjournal = "The American Mathematical Monthly", keywords = "approximation to limiting values; binomial coefficients; factorials; Stirling's formula", ZMclass = "*05A10 Combinatorial functions 40A25 Approximation to limiting values 26A09 Elementary functions of one real variable 41A60 Asymptotic problems in approximation", ZMnumber = "0786.05007", ZMreviewer = "D. Acu (Sibiu)", } @Article{Marsaglia:1990:RNG, author = "George Marsaglia and B. Narasimhan and Arif Zaman", title = "A random number generator for {PC}'s", journal = j-COMP-PHYS-COMM, volume = "60", number = "3", pages = "345--349", year = "1990", CODEN = "CPHCBZ", ISSN = "0010-4655", MRclass = "65C10", MRnumber = "1 076 268", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", fjournal = "Computer Physics Communications. An International Journal and Program Library for Computational Physics and Physical Chemistry", ZMclass = "*65C10 Random number generation", ZMnumber = "0997.65510", } @Article{Marsaglia:1990:TUR, author = "George Marsaglia and Arif Zaman and Wai Wan Tsang", title = "Toward a universal random number generator", journal = j-STAT-PROB-LETT, volume = "9", number = "1", pages = "35--39", year = "1990", CODEN = "SPLTDC", ISSN = "0167-7152", MRclass = "65C10", MRnumber = "91a:65008", bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/1990.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", abstract-1 = "This paper presents a ``universal'' random number generator that is able to produce the same sequence of random variables in a wide variety of computers and that passes some tests of randomness and independence. The generator combines two different generators: a lagged-Fibonacci generator $F(97,33.\cdot)$ and a simple arithmetic sequence for the prime modulus $2^{24}-3$. Results of a randomness test are presented and a Fortran implementation of the generator is suggested.", abstract-2 = "This article describes an approach towards a random number generator that passes all of the stringent tests for randomness we have put to it, and that is able to produce exactly the same sequence of uniform random variables in a wide variety of computers, including TRS80, Apple, Mackintosh, Commodore, Kaypro, IBM PC, AT, PC and AT clones, Sun, Vax, IBM 360/370, 3090, Amdahl, CDC Cyber and even 205 ETA supercomputers.", fjournal = "Statistics \& Probability Letters", keywords = "arithmetic sequence; Fortran implementation; independence test; lagged-Fibonacci generator; randomness test; universal random number generator", ZMclass = "*65C10 Random number generation", ZMnumber = "0692.65001", ZMreviewer = "K. Uosaki", } @Article{Zaman:1990:RSS, author = "Arif Zaman and George Marsaglia", title = "Random Selection of Subsets with Specified Element Probabilities", journal = j-COMM-STAT-THEORY-METH, volume = "19", number = "11", pages = "4419--4434", month = "????", year = "1990", CODEN = "CSTMDC", ISSN = "0361-0926", bibdate = "Thu Aug 05 06:44:44 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, } @Article{Marsaglia:1991:NCR, author = "George Marsaglia and Arif Zaman", title = "A new class of random number generators", journal = j-ANN-APPL-PROBAB, volume = "1", number = "3", pages = "462--480", month = "????", year = "1991", CODEN = "????", ISSN = "1050-5164", MRclass = "65C10", MRnumber = "92h:65009", MRreviewer = "Renata Rotondi", bibdate = "Mon Aug 02 11:01:47 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", abstract = "We introduce a new class of generators of two types: add-with-carry and subtract-with-borrow. Related to lagged-Fibonacci generators, the new class has interesting underlying theory, astonishingly long periods and provable uniformity for full sequences. Among several that we mention, we recommend particularly promising ones that will generate a sequence of 2e1751 bits.", acknowledgement = ack-nhfb, fjournal = "The Annals of Applied Probability", keywords = "add with carry generator; lagged Fibonacci generator; Monte Carlo methods; numerical examples; random number generators; subtract-with-borrow generators; very long period sequences", ZMclass = "*65C10 Random number generation 65C05 Monte Carlo methods", ZMnumber = "0733.65005", ZMreviewer = "M. Cugiani (Milano)", } @Article{Marsaglia:1991:NGR, author = "George Marsaglia", title = "Normal ({Gaussian}) Random Variables for Supercomputers", journal = j-J-SUPERCOMPUTING, volume = "5", number = "1", pages = "49--55", month = jun, year = "1991", CODEN = "JOSUED", ISSN = "0920-8542", bibdate = "Mon Jun 2 19:03:29 MDT 1997", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/jsuper.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, affiliation = "Dept. of Stat., Florida State Univ., Tallahassee, FL, USA", classification = "C1140G (Monte Carlo methods); C1140Z (Other and miscellaneous); C5440 (Multiprocessor systems and techniques); C7310 (Mathematics)", corpsource = "Dept. of Stat., Florida State Univ., Tallahassee, FL, USA", keywords = "efficient constant-time methods; exponential random variables; Gaussian random variables; Monte Carlo methods; Monte Carlo studies; normal distribution function; parallel machines; parallel operations; probability; statistical analysis; supercomputers", treatment = "P Practical", } @InCollection{Marsaglia:1992:MRN, author = "George Marsaglia", title = "The mathematics of random number generators", crossref = "Burr:1992:UEN", pages = "73--90", year = "1992", MRclass = "11K45 (65C10)", MRnumber = "94a:11119", MRreviewer = "R. G. Stoneham", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", series = "Proc. Sympos. Appl. Math.", abstract = "[For the entire collection see Zbl 0759.00006.]\par This paper first describes the role of number theory for the three most common classes of random number generators such as congruential, shift- register, and lagged-Fibonacci generators. A condition characterizing full-period sequences for shift-register generators is given its proof sketched, which also plays a role establishing the periods of lagged- Fibonacci generators. Then, more details are given for the mathematics of a new class of random number generators with quite long periods, called `add-with-carry' and `subtract-with-borrow' generators [the author and {\it A. Zaman}, Ann. Appl. Probab., 1, No. 3, 462--480 (1991; Zbl 0733.65005)]. A table listing examples of some of the most common random number generators including the classes mentioned above is given at the end of this paper.", keywords = "add-with-carry generator; congruential generators; lagged-Fibonacci generators; number theory; random number generators; shift-register generators; subtract-with-borrow generator", ZMclass = "*65C10 Random number generation 11K45 Pseudo-random numbers, etc. 11A07 Congruences, etc. 11A63 Radix representation", ZMnumber = "0776.65005", ZMreviewer = "K. Uosaki (Tottori)", } @TechReport{Marsaglia:1993:KG, author = "George Marsaglia and Arif Zaman", title = "The {KISS} generator", type = "Technical report", number = "??", institution = "Department of Statistics, Florida State University", address = "Tallahassee, FL, USA", month = "????", year = "1993", bibdate = "Sat Mar 08 15:05:47 2008", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, remark = "Check address: some citations show University of Florida, Gainesville, but the lead author worked at FSU. I cannot find this report in either the FSU or UF libraries, or their Departments of Statistics.", } @Article{Marsaglia:1993:MTR, author = "G. Marsaglia and Arif Zaman", title = "Monkey Tests for Random Number Generators", journal = j-COMP-MATH-APPL, volume = "26", number = "9", pages = "1--10", month = nov, year = "1993", CODEN = "CMAPDK", ISSN = "0097-4943, 0898-1221", MRclass = "65C10", MRnumber = "1 236 767", bibdate = "Mon Aug 02 10:36:54 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", abstract = "This paper describes some simple but sophisticated tests of suitability of certain random number generators (RNG's). The generators are used to provide the random keystrokes. The overlapping $m$-tuples of successive elements in random sequences are used for assessing both uniformity and independence in the output of a random number generator.\par One is CAT test: RNG has a typewriter with 26 upper-case letters and how many keystrokes needed to spell CAT is tested. The others are OPSO (Overlapping-Pairs-Sparse-Occupancy), OTSO (Overlapping-Triples-Sparse- Occupancy), OQSO (Overlapping-Quadruples-Sparse-Occupancy) and DNA tests: how many missing $k$-letter words in a long string of $n$ random keystrokes from an alphabet of $\alpha$ letters are tested.\par Examples of RNG's in classes of congruential generators, shift register generators, lagged Fibonacci generators, add-with-carry and subtract-and- carry generators and combination generators, passing these tests are presented.", acknowledgement = ack-nhfb, fjournal = "Computers \& Mathematics with Applications. An International Journal", keywords = "congruential generators; lagged Fibonacci generators; monkey tests; Overlapping-Pairs-Sparse-Occupancy; Overlapping-Quadruples-Sparse-Occupancy; Overlapping-Triples-Sparse-Occupancy; random number generators; shift register generators; sparse-occupancy tests", ZMclass = "*65C10 Random number generation 11K45 Pseudo-random numbers, etc.", ZMnumber = "0788.65007", ZMreviewer = "K. Uosaki (Tottori)", } @Article{Marsaglia:1993:RCI, author = "George Marsaglia", title = "Technical Correspondence: Remarks on Choosing and Implementing Random Number Generators", journal = j-CACM, volume = "36", number = "7", pages = "105--108", month = jul, year = "1993", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Tue Jan 28 14:57:13 1997", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1990.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, } @InCollection{Marsaglia:1993:RNG, author = "George Marsaglia", title = "Random Number Generation", crossref = "Ralston:1993:ECS", pages = "1145--1148", year = "1993", bibdate = "Mon Aug 02 16:28:18 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, xxnote = "Text substantially rewritten from second edition \cite{Marsaglia:1983:RNG}.", } @Article{Marsaglia:1993:SIS, author = "G. Marsaglia and B. Narasimhan", title = "Simulating interpolation search", journal = j-COMP-MATH-APPL, volume = "26", number = "8", pages = "31--42", year = "1993", CODEN = "CMAPDK", ISSN = "0097-4943, 0898-1221", MRclass = "68P10", MRnumber = "94h:68041", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", fjournal = "Computers \& Mathematics with Applications. An International Journal", keywords = "efficient algorithm; interpolation search; searching ordered tables", ZMclass = "*68P10 Searching and sorting 65C99 Numerical simulation", ZMnumber = "0800.68353", } @Article{Marsaglia:1994:REI, author = "George Marsaglia and Arif Zaman and John C. W. Marsaglia", title = "Rapid evaluation of the inverse of the normal distribution function", journal = j-STAT-PROB-LETT, volume = "19", number = "4", pages = "259--266", year = "1994", CODEN = "SPLTDC", ISSN = "0167-7152", MRclass = "65U05", MRnumber = "1 278 658", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", abstract = "This is an interesting article with direct application in generating normal random variable by computer programs. The suggested applications are related to Monte Carlo simulation based on massively parallel systems or supercomputers. The idea is to replace larger programs with complicated computations and with difficulties in accuracy controlling by simpler arithmetic programs that use tabled constants. These seem to be the normal evolution since memory becomes cheaper and cheaper.\par The authors compute the inverse of the cPhi function $$cPhi(x) = (2/\pi)^{1/2} \int^\infty_x \exp (-t^2/2) dt=u,$$ using a uniform random variable as input and the truncated Taylor series development of it. In order to increase the speed the coefficients of the truncated Taylor series $$x(u_0+h) = x(u_0) + x'(u_0) \cdot h + {1 \over 2} x''(u_0) \cdot h^2 + {1 \over 6} x'''(u_0) \cdot h^3,$$ are predetermined for 1024 points. And here comes another bright idea: the 1024 points are chosen based on the representation of the uniform random variable in modern computers as floating point variable of the form: $u=2^{-k} ((1/2) + (j/64)) + 2^{-k} \cdot (m/2^{24})$ with $0 \le k<32$, $0 \le j<32$ and $0 \le m<2^{18}$ and considering 32 bit representation.\par With this assumptions and the truncation to the third power of $h$ of the Taylor series, the authors show that the error does not exceed the limit of single precision accuracy. Furthermore the calculations are speeded up based on reducing multiplications. A number of FORTRAN programs are also presented in order to evaluate the complementary normal distribution function cPhi (several versions) with great accuracy, create the constant tables, and generate the normal distribution variable. These simple programs give the user the possibility to completely control the accuracy.", fjournal = "Statistics \& Probability Letters", keywords = "cPhi function; FORTRAN programs; massive parallel systems; Monte Carlo simulation; normal distribution function; normal random variable; supercomputers; truncated Taylor series", ZMclass = "*65C99 Numerical simulation 65C05 Monte Carlo methods 60-04 Machine computation, programs (probability theory) 60E05 General theory of probability distributions 62E17 Approximations to statistical distributions (nonasymptotic)", ZMnumber = "0798.65132", ZMreviewer = "A. Pasculescu (Bucuresti)", } @Article{Marsaglia:1994:SPV, author = "George Marsaglia and Arif Zaman", title = "Some portable very-long-period random number generators", journal = j-COMP-PHYSICS, volume = "8", number = "1", pages = "117--121", month = jan # "\slash " # feb, year = "1994", CODEN = "CPHYE2", DOI = "http://dx.doi.org/10.1063/1.168514", ISSN = "0894-1866", bibdate = "Mon Aug 02 17:54:20 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, remark = "ran2() range is [1,2147483562], with period about 2.3e+18. mzran13() has range[0,2147483647] and period about 2^125 = 4.25e37.", } @Article{Marsaglia:1995:RVI, author = "G. Marsaglia", title = "Random variables with independent integer and fractional parts", journal = j-STAT-NEERLANDICA, volume = "49", number = "2", pages = "133--137", year = "1995", ISSN = "0039-0402", MRclass = "62E10", MRnumber = "96d:62013", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", abstract = "For random variables with independent integer and fractional parts a canonical form is given for those with positive differentiable densities, and a condition ensuring exponentiality is made less restrictive.", fjournal = "Statistica Neerlandica. Journal of the Netherlands Society for Statistics and Operations Research", keywords = "canonical form; characterizations; exponential distribution; independent digits; independent integer and fractional parts; positive differentiable densities", ZMclass = "*62E10 Structure theory of statistical distributions 60E05 General theory of probability distributions", ZMnumber = "0831.62015", } @TechReport{Marsaglia:1996:DBT, author = "George Marsaglia", title = "{DIEHARD}: {A} Battery of Tests of Randomness", type = "Technical report", number = "????", institution = "Florida State University", address = "Tallahassee, FL, USA", year = "1996", bibdate = "Mon Aug 02 10:51:00 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", URL = "http://euler.bd.psu.edu/~naras/diehard/snapshots.html; http://stat.fsu.edu/~geo/", acknowledgement = ack-nhfb, } @Article{Marsaglia:1998:MPMa, author = "George Marsaglia and Wai Wan Tsang", title = "The {Monty Python} Method for Generating Gamma Variables", journal = j-J-STAT-SOFT, volume = "3", number = "3", pages = "1--8", year = "1998", CODEN = "JSSOBK", ISSN = "1548-7660", bibdate = "Sun Nov 17 22:35:43 2002", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/jstatsoft.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", URL = "http://www.jstatsoft.org/v03/i03; http://www.jstatsoft.org/v03/i03/GERMGAM.PDF; http://www.jstatsoft.org/v03/i03/GERMGAM.PS; http://www.jstatsoft.org/v03/i03/updates", abstract = "The Monty Python Method for generating random variables takes a decreasing density, cuts it into three pieces, then, using area-preserving transformations, folds it into a rectangle of area $1$. A random point $(x,y)$ from that rectangle is used to provide a variate from the given density, most of the time as $x$ itself or a linear function of $x$. The decreasing density is usually the right half of a symmetric density.\par The Monty Python method has provided short and fast generators for normal, $t$ and von Mises densities, requiring, on the average, from $1.5$ to $1.8$ uniform variables. In this article, we apply the method to non-symmetric densities, particularly the important gamma densities. We lose some of the speed and simplicity of the symmetric densities, but still get a method for variates that is simple and fast enough to provide beta variates in the form $\gamma_a=(\gamma_a + \gamma_b)$. We use an average of less than $1.7$ uniform variates to produce a gamma variate whenever $\alpha \geq 1$. Implementation is simpler and from three to five times as fast as a recent method reputed to be the best for changing $\alpha$s.", acknowledgement = ack-nhfb, } @Article{Marsaglia:1998:MPMb, author = "George Marsaglia and Wai Wan Tsang", title = "The {Monty Python} method for generating random variables", journal = j-TOMS, volume = "24", number = "3", pages = "341--350", month = sep, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65C10 (60E99)", MRnumber = "99k:65014", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/toms.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://www.acm.org/pubs/contents/journals/toms/1998-24/; MathSciNet database", URL = "http://doi.acm.org/10.1145/292395.292453; http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p341-marsaglia/", abstract = "We suggest an interesting and fast method for generating normal, exponential, $t$, von Mises, and certain other important random variables used in Monte Carlo studies. The right half of a symmetric density is cut into pieces, then, using simple area-preserving transformations, reassembled into a rectangle from which the $x$-coordinate---or a linear function of the $x$-coordinate---of a random point provides the required variate. To illustrate the speed and simplicity of the Monty Python method, we provide a small C program, self-contained, for rapid generation of normal (Gaussian) variables. It is self-contained in the sense that required uniform variates are generated in-line, as pairs of 16-bit integers by means of the remarkable new multiply-with-carry method.", acknowledgement = ack-nhfb, fjournal = "Association for Computing Machinery. Transactions on Mathematical Software", keywords = "$t$ variates; algorithms; Monte Carlo studies; Monty Python method; normal variates; random variable generation; theory; von Mises variates", subject = "{\bf G.3} Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf I.6.1} Computing Methodologies, SIMULATION AND MODELING, Simulation Theory.", ZMclass = "*65C10 Random number generation 65C05 Monte Carlo methods", ZMnumber = "0930.65002", } @TechReport{Marsaglia:2000:MRN, author = "George Marsaglia", title = "The Monster, {A} Random Number Generator with Period over $10^{2857}$ Times as Long as the Previously Touted Longest-period One", type = "Technical report", number = "????", institution = "Florida State University", address = "Tallahassee, FL, USA", month = "????", year = "2000", bibdate = "Mon Aug 02 10:39:48 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, } @Article{Marsaglia:2000:SMG, author = "George Marsaglia and Wai Wan Tsang", title = "A simple method for generating gamma variables", journal = j-TOMS, volume = "26", number = "3", pages = "363--372", year = "2000", CODEN = "ACMSCU", DOI = "http://doi.acm.org/10.1145/358407.358414", ISSN = "0098-3500", MRclass = "65C10 (65C60)", MRnumber = "2001k:65015", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/toms.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://www.acm.org/pubs/contents/journals/toms/; MathSciNet database", fjournal = "Association for Computing Machinery. Transactions on Mathematical Software", } @Article{Marsaglia:2000:ZMG, author = "George Marsaglia and Wai Wan Tsang", title = "The ziggurat method for generating random variables", journal = j-J-STAT-SOFT, volume = "5", number = "8", pages = "1--7", year = "2000", CODEN = "JSSOBK", ISSN = "1548-7660", bibdate = "Sun Nov 17 22:35:43 2002", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/jstatsoft.bib; ftp://ftp.math.utah.edu/pub/tex/bib/matlab.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", URL = "http://www.jstatsoft.org/v05/i08; http://www.jstatsoft.org/v05/i08/rnorrexp.c; http://www.jstatsoft.org/v05/i08/updates; http://www.jstatsoft.org/v05/i08/ziggurat.pdf", abstract = "We provide a new version of our ziggurat method for generating a random variable from a given decreasing density. It is faster and simpler than the original, and will produce, for example, normal or exponential variates at the rate of 15 million per second with a C version on a 400MHz PC. It uses two tables, integers $k_i$ and reals $w_i$. Some 99\% of the time, the required $x$ is produced by: Generate a random 32-bit integer $j$ and let $i$ be the index formed from the rightmost 8 bits of $j$. If $j < k_i$ return $x = j \times w_i$.\par We illustrate with C code that provides for inline generation of both normal and exponential variables, with a short procedure for setting up the necessary tables.", acknowledgement = ack-nhfb, annote = "This algorithm is used in Matlab's randn() function for generating normally-distributed pseudo-random numbers; see \cite{Moler:2001:CCN}.", } @Misc{Marsaglia:2002:RGB, author = "George Marsaglia", title = "Re: *good* 64-bit random-number generator", howpublished = "Posting to the {\tt sci.crypt.random-numbers} news group", day = "3", month = sep, year = "2002", bibdate = "Sat Mar 08 15:04:15 2008", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", URL = "http://groups.google.ws/group/comp.sys.sun.admin/browse_thread/thread/683ff52120e5b4d/b53ccad5aa5d6017", acknowledgement = ack-nhfb, } @Article{Marsaglia:2002:SDP, author = "George Marsaglia and Wai Wan Tsang", title = "Some Difficult-to-pass Tests of Randomness", journal = j-J-STAT-SOFT, volume = "7", number = "3", pages = "1--8", year = "2002", CODEN = "JSSOBK", ISSN = "1548-7660", bibdate = "Sun Nov 17 22:35:43 2002", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cryptography2000.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", URL = "http://www.jstatsoft.org/v07/i03; http://www.jstatsoft.org/v07/i03/tuftests.c; http://www.jstatsoft.org/v07/i03/tuftests.pdf; http://www.jstatsoft.org/v07/i03/updates", abstract = "We describe three tests of randomness --- tests that many random number generators fail. In particular, all congruential generators --- even those based on a prime modulus --- fail at least one of the tests, as do many simple generators, such as shift register and lagged Fibonacci. On the other hand, generators that pass the three tests seem to pass all the tests in the Diehard Battery of Tests.\par Note that these tests concern the randomness of a generator's output as a sequence of independent, uniform 32-bit integers. For uses where the output is converted to uniform variates in $[0,1)$, potential flaws of the output as integers will seldom cause problems after the conversion. Most generators seem to be adequate for producing a set of uniform reals in $[0,1)$, but several important applications. notably in cryptography and number theory --- for example, establishing probable primes, complexity of factoring algorithms, random partitions of large integers --- may require satisfactory performance on the kinds of tests we describe here.", acknowledgement = ack-nhfb, } @Article{Marsaglia:2003:EKD, author = "George Marsaglia and Wai Wan Tsang and Jingbo Wang", title = "Evaluating {Kolmogorov}'s Distribution", journal = j-J-STAT-SOFT, volume = "8", number = "18", pages = "1--4", year = "2003", CODEN = "JSSOBK", ISSN = "1548-7660", bibdate = "Tue Dec 16 17:06:19 2003", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", URL = "http://www.jstatsoft.org/v08/i18; http://www.jstatsoft.org/v08/i18/k.pdf", abstract = "Kolmogorov's goodness-of-fit measure, $D_n$, for a sample CDF has consistently been set aside for methods such as the $D_n^+$ or $D_n^-$; of Smirnov, primarily, it seems, because of the difficulty of computing the distribution of $D_n$. As far as we know, no easy way to compute that distribution has ever been provided in the 70+ years since Kolmogorov's fundamental paper. We provide one here, a C procedure that provides $\mbox{Pr}(D_n < d)$ with 13--15 digit accuracy for $n$ ranging from $2$ to at least $16000$. We assess the (rather slow) approach to limiting form, and because computing time can become excessive for probabilities $> 0.999$ with $n$'s of several thousand, we provide a quick approximation that gives accuracy to the 7th digit for such cases.", acknowledgement = ack-nhfb, } @Article{Marsaglia:2003:RNG, author = "George Marsaglia", title = "Random Number Generators", journal = j-J-MOD-APPL-STAT-METH, volume = "2", number = "1", pages = "2--13", month = may, year = "2003", CODEN = "????", ISSN = "1538-9472", bibdate = "Wed Dec 17 08:26:46 2003", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", URL = "http://stat.fsu.edu/pub/diehard/; http://tbf.coe.wayne.edu/jmasm/; http://www.csis.hku.hk/~diehard/", abstract = "The author discusses some promising new random number generators, as well as formulates the mathematical basis that makes them random variables in the same sense as more familiar ones in probability and statistics, emphasizing his view that randomness exists only in the sense of mathematics. He discusses the need for adequate seeds that provide the axioms for that mathematical basis, and gives examples from Law and Gaming, where inadequacies have led to difficulties. He also describes new versions of the widely used Diehard Battery of Tests of Randomness.", acknowledgement = ack-nhfb, keywords = "Random number generator, Diehard Test", remark = "This paper contains a nice survey of recommended generators, a recipe for recovering the multiplier and addend of linear congruential generators (p. 4, ``Cracking a Congruential RNG''), information on a direct floating-point RNG, and discussion of the new revision of the Diehard Test Suite.", } @Article{Marsaglia:2003:TOS, author = "George Marsaglia", title = "Technical opinion: Seeds for random number generators: Techniques for choosing seeds for social and scientific applications of random number generators", journal = j-CACM, volume = "46", number = "5", pages = "90--93", month = may, year = "2003", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed Sep 3 17:06:36 MDT 2003", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm2000.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://www.acm.org/pubs/contents/journals/cacm/", acknowledgement = ack-nhfb, } @Article{Marsaglia:2003:XR, author = "George Marsaglia", title = "Xorshift {RNGs}", journal = j-J-STAT-SOFT, volume = "8", number = "14", pages = "1--6", year = "2003", CODEN = "JSSOBK", ISSN = "1548-7660", bibdate = "Tue Dec 16 17:06:19 2003", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", note = "See \cite{Brent:2004:NMX} for corrections and the equivalence of xorshift generators and the well-understood linear feedback shift register generators. See \cite{Panneton:2005:XRN} for detailed analysis.", URL = "http://www.jstatsoft.org/v08/i14; http://www.jstatsoft.org/v08/i14/xorshift.pdf", abstract = "Description of a class of simple, extremely fast random number generators (RNGs) with periods $2^k - 1$ for $k = 32, 64, 96, 128, 160, 192$. These RNGs seem to pass tests of randomness very well.", acknowledgement = ack-nhfb, } @Article{Brent:2004:NMX, author = "Richard P. Brent", title = "Note on {Marsaglia}'s Xorshift Random Number Generators", journal = j-J-STAT-SOFT, volume = "11", number = "5", pages = "1--5", month = "", year = "2004", CODEN = "JSSOBK", ISSN = "1548-7660", bibdate = "Sat Dec 04 09:18:40 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", note = "See \cite{Marsaglia:2003:XR,Panneton:2005:XRN}. This article shows the equivalence of xorshift generators and the well-understood linear feedback shift register generators.", URL = "http://www.jstatsoft.org/counter.php?id=101&url=v11/i05/v11i05.pdf&ct=1", accepted = "2004-08-25", acknowledgement = ack-nhfb, submitted = "2004-07-07", } @Article{Marsaglia:2004:BUR, author = "George Marsaglia and Wai Wan Tsang", title = "The 64-bit universal {RNG}", journal = j-STAT-PROB-LETT, volume = "66", number = "2", pages = "183--187", year = "2004", CODEN = "SPLTDC", DOI = "http://dx.doi.org/10.1016/j.spl.2003.11.001", ISSN = "0167-7152", MRclass = "65C10", MRnumber = "2 029 733", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; MathSciNet database", abstract = "We describe a random number generator that produces uniform $[0,1)$ variates directly, as 64-bit floating point numbers, without the customary floating of integers. Using only subtraction and tests on magnitude, the method is readily implemented and should, given the same seed values, produce exactly the same random numbers with most programming languages. The resulting numbers have a very long period ($\approx 2^{202}$ or $10^{61}$) and apparently excellent randomness---supported by extensive testing.", fjournal = "Statistics \& Probability Letters", keywords = "64-bit floating point; Random number generators; Seeds", URL = "http://www.doornik.com/research/randomdouble.pdf", ZMclass = "*62-99 Statistics", ZMnumber = "02041513", } @Article{Marsaglia:2004:EAD, author = "George Marsaglia and John Marsaglia", title = "Evaluating the {Anderson--Darling} Distribution", journal = j-J-STAT-SOFT, volume = "9", number = "2", pages = "1--5", day = "25", month = feb, year = "2004", CODEN = "JSSOBK", ISSN = "1548-7660", bibdate = "Wed Feb 25 11:20:56 2004", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/jstatsoft.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", URL = "http://www.jstatsoft.org/v09/i02/ad.pdf; http://www.jstatsoft.org/v09/i02/ADinf.c; http://www.jstatsoft.org/v09/i02/AnDarl.c", acknowledgement = ack-nhfb, } @Article{Marsaglia:2004:END, author = "George Marsaglia", title = "Evaluating the Normal Distribution", journal = j-J-STAT-SOFT, volume = "11", number = "4", pages = "1--7", month = "", year = "2004", CODEN = "JSSOBK", ISSN = "1548-7660", bibdate = "Sat Dec 04 09:18:40 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", URL = "http://www.jstatsoft.org/counter.php?id=100&url=v11/i04/cphi.pdf&ct=1", accepted = "2004-07-18", acknowledgement = ack-nhfb, remark = "This article exhibits accurate, compact, and fast algorithms for computation of the normal distribution function and the complementary normal distribution, which have a simple relation to the error function and the complementary error function. They appear to be improvements on almost all previously-published algorithms for these functions. However, closer study shows that the complementary normal distribution function has an unchecked out-of-bounds array access for |x| >= 17, and its Taylor series sum has poor convergence because the tabulated intervals are twice too wide. The Taylor series sum for the normal distribution function is expanded around x = 0, and thus has poor convergence for large |x|. Neither function takes into account the accuracy loss when the computed result is the larger of the two (their sum is one, and their range is [-Infinity,+Infinity]), although the text discusses the problem. The article also discusses the historical origin of the term ``error function'', tracing it to J. W. Glaisher in 1871.", submitted = "2004-06-05", } @Article{Marsaglia:2004:FGD, author = "George Marsaglia and Wai Wan Tsang and Jingbo Wang", title = "Fast Generation of Discrete Random Variables", journal = j-J-STAT-SOFT, volume = "11", number = "3", pages = "1--8", month = "", year = "2004", CODEN = "JSSOBK", ISSN = "1548-7660", bibdate = "Sat Dec 04 09:18:40 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", URL = "http://www.jstatsoft.org/counter.php?id=99&url=v11/i03/discrete.pdf&ct=1", accepted = "2004-07-12", acknowledgement = ack-nhfb, submitted = "2004-06-05", } %%% ==================================================================== %%% These entries must come last because they are cross-referenced %%% by others above. @Book{Ralston:1976:ECS, editor = "Anthony Ralston and Chester L. Meek", title = "Encyclopedia of computer science", publisher = "Petrocelli\slash Charter", address = "New York, NY, USA", pages = "xxviii + 1523", year = "1976", ISBN = "0-88405-321-0", LCCN = "QA76.15 .E55 1976", bibdate = "Mon Aug 02 16:32:11 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, } @Proceedings{Kozesnik:1964:TTP, editor = "Jaroslav Ko{\v{z}}e{\v{s}}n{\'\i}k", booktitle = "Transactions of the third Prague conference on information theory, statistical decision functions, random processes held at Liblice near Prague, from June 5 to 13, 1962", title = "Transactions of the third Prague conference on information theory, statistical decision functions, random processes held at Liblice near Prague, from June 5 to 13, 1962", publisher = "Czechoslovak academy of science", address = "Prague, Czechoslovakia", pages = "846", year = "1964", LCCN = "????", bibdate = "Thu Aug 05 05:58:29 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", note = "In memory of RNDr. Antonin Spacek.", acknowledgement = ack-nhfb, } @Proceedings{Kozesnik:1967:TFP, editor = "Jaroslav Ko{\v{z}}e{\v{s}}n{\'\i}k", booktitle = "Transactions of the fourth Prague conference on information theory, statistical decision functions, random processes, held at Prague, from August 31 to September 11, 1965", title = "Transactions of the fourth Prague conference on information theory, statistical decision functions, random processes, held at Prague, from August 31 to September 11, 1965", publisher = "Academia", address = "Prague, Czechoslovakia", pages = "725", year = "1967", LCCN = "", bibdate = "Thu Aug 05 06:05:35 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, } @Proceedings{Talbot:1969:ATP, editor = "A. (Alan) Talbot", booktitle = "Approximation theory: proceedings of a symposium held at Lancaster, July 1969", title = "Approximation theory: proceedings of a symposium held at Lancaster, July 1969", publisher = "Academic Press", address = "London", pages = "viii + 356", year = "1969", ISBN = "0-12-682250-6", LCCN = "QA221 .A66", bibdate = "Thu Aug 05 06:10:49 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, remark = "Papers from a conference held at the Mathematics Department, University of Lancaster 21--25 July 1969.", } @Proceedings{Zaremba:1972:ANT, editor = "S. K. Zaremba", booktitle = "Applications of Number Theory to Numerical Analysis = {Applications} de la th{\'e}orie des nombres {\`a} l'analyse num{\'e}rique. Proceedings of the symposium at the {Centre for Research in Mathematics, University of Montreal, September 9--14, 1971}", title = "Applications of Number Theory to Numerical Analysis = {Applications} de la th{\'e}orie des nombres {\`a} l'analyse num{\'e}rique. Proceedings of the symposium at the {Centre for Research in Mathematics, University of Montreal, September 9--14, 1971}", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "xii + 489", year = "1972", ISBN = "0-12-775950-6", LCCN = "QA297 .A67", bibdate = "Mon Aug 02 10:53:03 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, language = "French and English", } @Proceedings{Saleh:1975:PSS, editor = "A. K. Md. Ehsanes Saleh", booktitle = "Proceedings of the Symposium on Statistics and Related Topics: October 24--26, 1974, Carleton University, Ottawa", title = "Proceedings of the Symposium on Statistics and Related Topics: October 24--26, 1974, Carleton University, Ottawa", volume = "12", publisher = "Carleton University", address = "Ottawa, ON, Canada", pages = "437", year = "1975", ISBN = "????", ISSN = "0318-6288", LCCN = "QA276.A1 S92 1974", bibdate = "Thu Aug 05 06:14:23 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", series = "Carleton mathematical lecture notes", acknowledgement = ack-nhfb, } @Book{Ralston:1983:ECS, editor = "Anthony Ralston and Edwin D. {Reilly, Jr.}", booktitle = "Encyclopedia of Computer Science and Engineering", title = "Encyclopedia of Computer Science and Engineering", publisher = pub-VAN-NOSTRAND-REINHOLD, address = pub-VAN-NOSTRAND-REINHOLD:adr, edition = "Second", pages = "xxix + 1664", year = "1983", ISBN = "0-442-24496-7", LCCN = "QA76.15 .E48 1983", bibdate = "Mon Aug 02 10:58:31 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, } @Proceedings{Billard:1985:CSS, editor = "L. (Lynne) Billard", booktitle = "Computer science and statistics: proceedings of the Sixteenth Symposium on the Interface, Atlanta, Georgia, March 1984", title = "Computer science and statistics: proceedings of the Sixteenth Symposium on the Interface, Atlanta, Georgia, March 1984", publisher = pub-ELS, address = pub-ELS:adr, pages = "xi + 296", year = "1985", ISBN = "0-444-87725-8", LCCN = "QA276.4 .S95 1984", bibdate = "Thu Dec 18 13:41:50 2003", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, } @Proceedings{Gleser:1989:CPS, editor = "Leon Jay Gleser and others", booktitle = "Contributions to probability and statistics: essays in honor of Ingram Olkin", title = "Contributions to probability and statistics: essays in honor of Ingram Olkin", publisher = pub-SV, address = pub-SV:adr, pages = "x + 505", year = "1989", ISBN = "0-387-97076-2, 3-540-97076-2", LCCN = "QA273.18 .C683 1989", bibdate = "Thu Aug 05 06:19:18 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, } @Proceedings{Burr:1992:UEN, editor = "Stefan A. Burr and George E. Andrews and others", booktitle = "The unreasonable effectiveness of number theory: American Mathematical Society short course, August 6--7, 1991, Orono, Maine", title = "The unreasonable effectiveness of number theory: American Mathematical Society short course, August 6--7, 1991, Orono, Maine", volume = "46", publisher = pub-AMS, address = pub-AMS:adr, pages = "x + 156", year = "1992", ISBN = "0-8218-5501-8", LCCN = "QA241 .U67 1992", bibdate = "Thu Aug 05 06:26:07 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", series = "Proceedings of symposia in applied mathematics", acknowledgement = ack-nhfb, } @Book{Ralston:1993:ECS, editor = "Anthony Ralston and Edwin D. {Reilly, Jr.}", booktitle = "Encyclopedia of Computer Science and Engineering", title = "Encyclopedia of Computer Science and Engineering", publisher = pub-VAN-NOSTRAND-REINHOLD, address = pub-VAN-NOSTRAND-REINHOLD:adr, edition = "Third", pages = "xxv + 1558", year = "1993", ISBN = "0-442-27679-6", LCCN = "QA76.15 .E48 1993", bibdate = "Mon Aug 02 10:58:31 2004", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, } @Article{Marsaglia:2005:MGF, author = "George Marsaglia", title = "Monkeying with the Goodness-of-Fit Test", journal = j-J-STAT-SOFT, volume = "14", number = "13", pages = "1--4", day = "20", month = sep, year = "2005", CODEN = "JSSOBK", ISSN = "1548-7660", bibdate = "Mon Dec 12 11:09:58 2005", URL = "http://www.jstatsoft.org/counter.php?id=138&url=v14/i13/v14i13.pdf&ct=1; http://www.jstatsoft.org/counter.php?id=138&url=v14/i13&ct=2", abstract = "The familiar $\sumP(\textrm{OBS} - \textrm{EXP})^2/\textrm{EXP}$ goodness-of-fit measure is commonly used to test whether an observed sequence came from the realization of $n$ independent identically distributed (iid) discrete random variables. It can be quite effective for testing for identical distribution, but is not suited for assessing independence, as it pays no attention to the order in which output values are received.\par This note reviews a way to adjust or tamper, that is, monkey-with the classical test to make it test for independence as well as identical distribution in short, to test for both the i's in iid, using monkey tests similar to those in the Diehard Battery of Tests of Randomness (Marsaglia 1995).", accepted = "2005-09-20", acknowledgement = ack-nhfb, keywords = "goodness of fit; $\chi^2$; monkey tests; overlapping m-tuples", submitted = "2005-05-01", } @Article{Marsaglia:2006:RNV, author = "George Marsaglia", title = "Ratios of Normal Variables", journal = j-J-STAT-SOFT, volume = "16", number = "4", pages = "1--10", month = may, year = "2006", CODEN = "JSSOBK", ISSN = "1548-7660", bibdate = "Fri Jul 4 10:54:15 MDT 2008", URL = "http://www.jstatsoft.org/v16/i04", abstract = "This article extends and amplifies on results from a paper of over forty years ago. It provides software for evaluating the density and distribution functions of the ratio $z/w$ for any two jointly normal variates $z$, $w$, and provides details on methods for transforming a general ratio $z/w$ into a standard form, $(a+x)/(b+y)$, with $x$ and $y$ independent standard normal and $a$, $b$ non-negative constants. It discusses handling general ratios when, in theory, none of the moments exist yet practical considerations suggest there should be approximations whose adequacy can be verified by means of the included software. These approximations show that many of the ratios of normal variates encountered in practice can themselves be taken as normally distributed. A practical rule is developed: If $a < 2.256$ and $4 < b$ then the ratio $(a+x)/(b+y)$ is itself approximately normally distributed with mean $\mu = a/(1.01b - 0.2713)$ and variance $\sigma^2 = (a^2 + 1)/(b^2 + 0.108b - 3.795) \mu^2$.", acknowledgement = ack-nhfb, pubdates = "Submitted 2006-03-07; Accepted 2006-05-11", } %%% ==================================================================== %%% Papers cross-referenced by Marsaglia bibliography entries, or %%% citing Marsaglia in their titles: @Article{Coveyou:1967:FAU, author = "R. R. Coveyou and R. D. MacPherson", title = "{Fourier} Analysis of Uniform Random Number Generators", journal = j-J-ACM, volume = "14", number = "1", pages = "100--119", month = jan, year = "1967", CODEN = "JACOAH", ISSN = "0004-5411", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", acknowledgement = ack-nhfb, annote = "A method of analysis of uniform random number generators is developed, applicable to almost all practical methods of generation. The method is that of Fourier analysis of the output sequences of such generators. With this tool it is possible to understand and predict relevant statistical properties of such generators and compare and evaluate such methods. Many such analyses and comparisons have been carried out.", descriptors = "Shift register sequences; method; spectral analysis; interdependence; multidimensional uniformity; RNG; test", } @Article{Pokhodzei:1983:OMM, author = "B. B. Pokhodze\u{\i}", title = "Optimality of the {Marsaglia} method for simulating discrete distributions", journal = "Vestnik Leningrad. Univ. Mat. Mekh. Astronom.", volume = "4", pages = "105--107", year = "1983", ISSN = "0024-0850", MRclass = "65C10", MRnumber = "85a:65015", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", abstract = "It is shown that after a small modification the famous {\it G. Marsaglia's} method [Commun. ACM 6, 37-38 (1963; Zbl 0112.084)] for generation of discrete distributions reduces to an optimal algorithm for transformation of random bits to random variables with given distribution.", classmath = "*60E99 Distribution theory in probability theory 65C10 Random number generation", fjournal = "Vestnik Leningradskogo Universiteta. Matematika, Mekhanika, Astronomiya", keywords = "Marsaglia's method; transformation of random bits to random variables with given distribution", language = "Russian. English summary", xxtitle = "On optimal {Marsaglia}'s method for simulating discrete distributions", ZMnumber = "0551.60020", } @Article{Retter:1984:CMM, author = "C. Retter", title = "Cryptanalysis of a {Maclaren-Marsaglia} System", journal = j-CRYPTOLOGIA, volume = "8", number = "2", pages = "97--108", month = apr, year = "1984", CODEN = "CRYPE6", ISSN = "0161-1194", bibdate = "Sat Nov 21 12:35:16 MST 1998", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cryptologia.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://www.dean.usma.edu/math/pubs/cryptologia/", note = "See also letters and responses, Cryptologia {\bf 8}, 1984, pp. 374--378.", acknowledgement = ack-nhfb, romanvolume = "VIII", } @Article{Retter:1985:KSA, author = "C. Retter", title = "Key-Search Attack on {Maclaren-Marsaglia} Systems", journal = j-CRYPTOLOGIA, volume = "9", number = "2", pages = "114--130", month = apr, year = "1985", CODEN = "CRYPE6", ISSN = "0161-1194", bibdate = "Sat Nov 21 12:35:16 MST 1998", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cryptologia.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://www.dean.usma.edu/math/pubs/cryptologia/", acknowledgement = ack-nhfb, romanvolume = "IX", } @Article{Eichenauer:1988:MLTb, author = "J{\"u}rgen Eichenauer and Harald Niederreiter", title = "On {Marsaglia}'s lattice test for pseudorandom numbers", journal = j-MANUSCR-MATH, volume = "62", number = "2", pages = "245--248", year = "1988", CODEN = "MSMHB2", ISSN = "0025-2611", MRclass = "65C10 (11K45)", MRnumber = "90c:65011", MRreviewer = "J. Patrick Lambert", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", abstract = "Nonlinear recursive congruential pseudorandom number equations with prime modulus and maximal period length are considered. The authors give characterizations for these generator which behave optimally with respect to Marsaglia's lattice test.", classmath = "*65C10 Random number generation; 11K99 Probabilistic theory", fjournal = "Manuscripta Mathematica", keywords = "Marsaglia's lattice test; maximal period length; Nonlinear recursive congruential pseudorandom number equations", language = "English", ZMnumber = "0663.65006", ZMreviewer = "R. F. Tichy", } @Article{Eichenauer:1988:MLTc, author = "J{\"u}rgen Eichenauer and Holger Grothe and J{\"u}rgen Lehn", title = "{Marsaglia}'s lattice test and non-linear congruential pseudo-random number generators", journal = j-METRIKA, volume = "35", number = "3/4", pages = "241--250", year = "1988", CODEN = "????", ISSN = "0026-1335 (print), 1435-926X (electronic)", MRclass = "65C10", bibsource = "ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib", abstract = "A recursive congruential non-additive generator of the form $(1)\quad x_{n+1}\equiv f(x_n)(mod p),$ $x_{n+1}\in {\bbfZ}_p$, $n\ge 0$, is considered, where p is a large prime number, ${\bbfZ}_p=\{0,1,...,p-1\}$, $x_0\in {\bbfZ}_p$, and f: ${\bbfZ}_p\to {\bbfZ}_p$ is a function such that (1) has maximal period length. The sequences of integers $\{x_i:$ $i\ge 0\}$ generated by (1) are divided into vectors of $d\ge 2$ consecutive numbers: $v^d_i=(x_i,...,x_{i+d-1})^T\in {\bbfZ}^d_p$ and let $w^d_i\equiv v_i^d-v^d_0(mod p),$ $i\ge 0$. For $d\le 3$, it is shown that $V^d={\bbfZ}^d_p,$ where $V^d=\{v\in {\bbfZ}^d_p\vert \quad v\equiv \sum^{p-1}_{i=1}z_iw^d_i(mod p);\quad z_1,...,z_{p-1}\in {\bbfZ}_p\}.$ In other words, (1) passes {\it G. Marsaglia}'s lattice test [Applications of number theory to numerical analysis, 249-285 (1972; Zbl 0266.65007)]. For $d\ge 4$ there are generators (1) which fail this test. It is also shown that the generators of a class of nonlinear generators introduced by the first and the third author [Stat. Hefte 27, 315-326 (1986; Zbl 0607.65001)] pass Marsaglia's lattice test for $d\le (p-1)/2$.", classmath = "*65C10 Random number generation", keywords = "Marsaglia's lattice test; nonlinear generators; pseudo random number generators; recursive congruential non-additive generator", language = "English", ZMnumber = "0653.65006", ZMreviewer = "R. Theodorescu", } @Article{Harmon:1988:AIM, author = "Marion G. Harmon and Ted P. baker", title = "An {Ada} Implementation of {Marsaglia}'s ``Universal'' Random Number Generator", journal = j-SIGADA-LETTERS, volume = "8", number = "2", pages = "110--112", month = mar # "\slash " # apr, year = "1988", CODEN = "AALEE5", ISSN = "0736-721X", bibdate = "Sat Aug 9 09:05:28 MDT 2003", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/sigada.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; ftp://ftp.uu.net/library/bibliography; http://portal.acm.org/; http://www.adahome.com/Resources/Bibliography/articles.ref", acknowledgement = ack-nhfb, keywords = "algorithms; design; languages; real numbers; theory", subject = "D.3.2 Software, PROGRAMMING LANGUAGES, Language Classifications, Ada \\ G.3 Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation", } @Article{Percus:1995:TAM, author = "Ora E. Percus and Paula A. Whitlock", title = "Theory and application of {Marsaglia}'s monkey test for pseudorandom number generators", journal = j-TOMACS, volume = "5", number = "2", pages = "87--100", month = apr, year = "1995", CODEN = "ATMCEZ", ISSN = "1049-3301", bibdate = "Thu Aug 7 12:05:30 MDT 2003", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/tomacs.bib; ftp://ftp.math.utah.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://dblp.uni-trier.de/db/journals/tomacs/tomacs5.html#PercusW95; http://www.acm.org/pubs/contents/journals/tomacs/", abstract = "The authors give a survey on theory and application of Marsaglia's monkey test for pseudo-random number generators. The aim of the test is to find out correlations between small subsequences of the full sequence of a pseudorandom number generator. For illustration, the test is used to investigate five known pseudorandom number generators.", acknowledgement = ack-nhfb, classmath = "*65C10 Random number generation 11K45 Pseudo-random numbers, etc.", keywords = "empirical tests; Marsaglia's monkey test; pseudorandom number generators", language = "English", oldlabel = "PercusW95", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/tomacs/PercusW95", ZMnumber = "0853.65009", ZMrevie