%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "1.73",
%%% date = "13 October 2017",
%%% time = "16:04:41 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 = "21589 6225 28538 288298",
%%% 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 (March 12, 1924--February
%%% 15, 2011), late Professor Emeritus of Pure
%%% and Applied Mathematics, Computer Science and
%%% Statistics, Washington State and Florida
%%% State University (Pullman, WA, USA, and
%%% 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 1.73, the year coverage looked
%%% like this:
%%%
%%% 1948 ( 1) 1971 ( 2) 1994 ( 4)
%%% 1949 ( 0) 1972 ( 4) 1995 ( 3)
%%% 1950 ( 0) 1973 ( 1) 1996 ( 1)
%%% 1951 ( 1) 1974 ( 4) 1997 ( 3)
%%% 1952 ( 1) 1975 ( 4) 1998 ( 3)
%%% 1953 ( 1) 1976 ( 3) 1999 ( 2)
%%% 1954 ( 2) 1977 ( 1) 2000 ( 5)
%%% 1955 ( 0) 1978 ( 1) 2001 ( 3)
%%% 1956 ( 0) 1979 ( 0) 2002 ( 2)
%%% 1957 ( 4) 1980 ( 2) 2003 ( 6)
%%% 1958 ( 0) 1981 ( 0) 2004 ( 6)
%%% 1959 ( 0) 1982 ( 0) 2005 ( 5)
%%% 1960 ( 3) 1983 ( 4) 2006 ( 2)
%%% 1961 ( 6) 1984 ( 4) 2007 ( 0)
%%% 1962 ( 7) 1985 ( 5) 2008 ( 0)
%%% 1963 ( 9) 1986 ( 1) 2009 ( 0)
%%% 1964 ( 14) 1987 ( 1) 2010 ( 2)
%%% 1965 ( 10) 1988 ( 5) 2011 ( 5)
%%% 1966 ( 1) 1989 ( 5) 2012 ( 1)
%%% 1967 ( 8) 1990 ( 5) 2013 ( 0)
%%% 1968 ( 4) 1991 ( 2) 2014 ( 1)
%%% 1969 ( 4) 1992 ( 4) 2015 ( 0)
%%% 1970 ( 5) 1993 ( 8) 2016 ( 1)
%%% 19xx ( 1)
%%%
%%% Article: 117
%%% Book: 6
%%% InCollection: 11
%%% InProceedings: 4
%%% MastersThesis: 1
%%% Misc: 9
%%% PhdThesis: 1
%%% Proceedings: 11
%%% TechReport: 41
%%% Unpublished: 2
%%%
%%% Total entries: 203
%%%
%%% 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.",
%%% }
%%% ====================================================================
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%%% ====================================================================
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@String{j-ANN-APPL-PROBAB = "Annals of applied probability"}
@String{j-ANN-MATH-STAT = "Annals of mathematical statistics"}
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Theoretical and Applied Statistics."}
@String{j-MONTE-CARLO-METHODS-APPL = "Monte Carlo Methods and Applications"}
@String{j-NEW-ENGLAND-J-MED = "The New England Journal of Medicine"}
@String{j-NUM-MATH = "Numerische Mathematik"}
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@String{j-PHYS-REV-LET = "Physical Review Letters"}
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%%% ====================================================================
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@String{pub-ACADEMIC:adr = "New York, NY, USA"}
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@String{pub-ACM:adr = "New York, NY 10036, USA"}
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@String{pub-WILEY:adr = "New York, NY, USA"}
%%% ====================================================================
%%% Bibliography entries, sort by year and citation label:
@MastersThesis{Marsaglia:1948:SSP,
author = "George Marsaglia",
title = "The structures of stochastic processes",
type = "Thesis ({M.A.})",
school = "The Ohio State University",
address = "Columbus, OH, USA",
pages = "??",
year = "1948",
bibdate = "Wed Jun 22 07:15:13 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{Marsaglia:1951:SPC,
author = "George Marsaglia",
title = "Stochastic Processes and Classes of Random Variables",
type = "{Ph.D.} thesis",
school = "The Ohio State University",
address = "Columbus, OH, USA",
pages = "46",
year = "1951",
bibdate = "Wed Jun 22 07:10:43 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://ezproxy.lib.utah.edu/docview/302068737?accountid=14677",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1953:NCD,
author = "George Marsaglia",
title = "A Note on the Compatibility of Distribution
Functions",
type = "Report",
number = "85",
institution = "Institute of Statistics, University of North
Carolina",
address = "Chapel Hill, NC, USA",
pages = "ii + 2",
day = "12",
month = nov,
year = "1953",
bibdate = "Tue Jun 21 19:20:14 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/get-tr-doc/pdf?AD=AD0029405",
acknowledgement = ack-nhfb,
remark = "Special report to the Office of Naval Research of work
at Chapel Hill under Project NR 042 031, Contract
N7-onr-28492, for research in probability and
statistics.",
}
@TechReport{Marsaglia:1954:ILCa,
author = "George Marsaglia",
title = "Iterated limits and the central limit theorem for
dependent variables",
type = "Special Report",
number = "93",
institution = "Institute of Statistics, University of North
Carolina",
address = "Chapel Hill, NC, USA",
pages = "ii + 7",
month = feb,
year = "1954",
bibdate = "Wed Nov 12 07:27:27 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0035146;
http://www.dtic.mil/dtic/tr/fulltext/u2/035146.pdf;
http://www.dtic.mil/get-tr-doc/pdf?AD=AD0035146",
acknowledgement = ack-nhfb,
remark = "Special report to the Office of Naval Research of work
at Chapel Hill under Project NR 042 031 for research in
probability and statistics.",
}
@Article{Marsaglia:1954:ILCb,
author = "George Marsaglia",
title = "Iterated limits and the central limit theorem for
dependent variables",
journal = j-PROC-AM-MATH-SOC,
volume = "5",
number = "6",
pages = "987--991",
month = dec,
year = "1954",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "60.0X",
MRnumber = "16,494e",
MRreviewer = "D. G. Kendall",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database; ZentralBlatt Math database",
ZMnumber = "0056.36102",
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
keywords = "Probability theory",
}
@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",
number = "3",
pages = "678--686",
month = sep,
year = "1957",
CODEN = "AASTAD",
DOI = "https://doi.org/10.1214/aoms/1177706879",
ISSN = "0003-4851",
MRclass = "62.0X",
MRnumber = "19,1095e",
MRreviewer = "M. Dwass",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
URL = "http://projecteuclid.org/euclid.aoms/1177706879",
ZMnumber = "0080.35502",
fjournal = "Annals of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
keywords = "Statistics",
ZMreviewer = "T. V. Narayana",
}
@TechReport{Marsaglia:1957:GLH,
author = "George Marsaglia",
title = "The General Linear Hypothesis",
type = "Statistical paper",
number = "2",
institution = "Departments of Economics, Statistics \& Commerce,
University of Rangoon",
address = "Rangoon, Burma",
month = "????",
year = "1957",
bibdate = "Wed Jun 22 06:56:59 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.worldcat.org/title/general-linear-hypothesis/oclc/27397695",
acknowledgement = ack-nhfb,
}
@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 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Thu Aug 05 08:58:22 2004",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
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,
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}
@TechReport{Marsaglia:1960:GED,
author = "George Marsaglia",
title = "On generating exponentially distributed random
variables",
type = "Report",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "??",
month = "????",
year = "1960",
bibdate = "Tue Jun 21 18:58:31 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1960:TDQ,
author = "George Marsaglia",
title = "Tables of the distribution of quadratic forms of ranks
two and three",
type = "Report",
number = "213",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "??",
month = "????",
year = "1960",
bibdate = "Wed Nov 12 07:42:28 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1960:TSR,
author = "George Marsaglia",
title = "Tables of {$ 1 / 2 \pi {\Tan }^{-1}(\lambda) $} and {$
{\Tan }^{-1}(\lambda) $} for $ \lambda = .0001, .0002,
\ldots {}, .9999 $, with some remarks on their use in
finding the normal probability measure of polygonal
regions",
type = "Report",
number = "D1-82-0078",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "??",
month = "????",
year = "1960",
bibdate = "Tue Jun 21 18:58:31 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
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",
month = sep,
year = "1961",
CODEN = "AASTAD",
DOI = "https://doi.org/10.1214/aoms/1177704983",
ISSN = "0003-4851",
MRclass = "65.15",
MRnumber = "23 \#B3122",
MRreviewer = "M. E. Muller",
bibdate = "Thu Dec 22 07:41:29 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
MathSciNet database",
URL = "http://projecteuclid.org/euclid.aoms/1177704983;
http://www.jstor.org/stable/2237849",
ZMnumber = "0139.35604",
abstract = "This note suggests that expressing a distribution
function as a mixture of suitably chosen distribution
functions leads to improved methods for generating
random variables in a computer. The idea is to choose a
distribution function which is close to the original
and use it most of the time, applying the correction
only infrequently. Mixtures allow this to be done in
probability terms rather than in the more elaborate
ways of conventional numerical analysis, which must be
applied every time.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematical Statistics",
HDnumber = "75",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
keywords = "probability theory",
}
@Article{Marsaglia:1961:GER,
author = "G. Marsaglia",
title = "Generating exponential random variables",
journal = j-ANN-MATH-STAT,
volume = "32",
number = "3",
pages = "899--900",
month = sep,
year = "1961",
CODEN = "AASTAD",
DOI = "https://doi.org/10.1214/aoms/1177704984",
ISSN = "0003-4851",
MRclass = "65.15",
MRnumber = "23 \#B3123",
MRreviewer = "M. E. Muller",
bibdate = "Thu Dec 22 07:41:41 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
MathSciNet database",
URL = "http://projecteuclid.org/euclid.aoms/1177704984;
http://www.jstor.org/stable/2237850",
ZMnumber = "0139.35603",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematical Statistics",
HDnumber = "76",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
keywords = "probability theory",
}
@TechReport{Marsaglia:1961:PGN,
author = "George Marsaglia",
title = "Procedures for Generating Normal Random Variables,
{II}",
type = "Mathematical note",
number = "243",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
month = oct,
year = "1961",
bibdate = "Tue Jun 21 18:56:22 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
abstract = "A method for generating a normal random variable in
terms of uniform random variables is described. The
method is based on representing a density function as a
mixture of simpler densities. It is fast and requires
little storage (60 constants). It is not quite as fast
as other methods, but it is simpler, with less chance
for prospective users being set adrift in a sea of
details",
acknowledgement = ack-nhfb,
HDnumber = "78",
}
@TechReport{Marsaglia:1961:RGR,
author = "G. Marsaglia",
title = "Remark on generating a random variable having a nearly
linear density function",
type = "Mathematical Note",
number = "242",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
year = "1961",
bibdate = "Mon Jun 27 15:17:02 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
HDnumber = "77",
}
@Article{Marsaglia:1961:SPT,
author = "George Marsaglia",
title = "Some probability theory associated with
clustered-rocket flights",
journal = j-PLANET-SPACE-SCI,
volume = "4",
number = "??",
pages = "194--201",
month = jan,
year = "1961",
CODEN = "PLSSAE",
DOI = "https://doi.org/10.1016/0032-0633(61)90132-5",
ISSN = "0032-0633 (print), 1873-5088 (electronic)",
ISSN-L = "0032-0633",
bibdate = "Wed Jun 22 06:45:09 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0032063361901325",
abstract = "The primary purpose of this note is to provide the
probability distribution of the amount of propellant
remaining in a cluster of rocket engines at the times
that the first and second burnouts occur. In addition,
various other random variables associated with the
random behavior of the engines of a cluster (pitch and
yaw moments, time between successive burnouts, etc.)
are discussed.",
acknowledgement = ack-nhfb,
fjournal = "Planetary and Space Science",
journal-URL = "http://www.sciencedirect.com/science/journal/00320633",
}
@TechReport{Marsaglia:1961:UDS,
author = "George Marsaglia",
title = "Uniform Distributions Over a Simplex",
type = "Mathematical note",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
month = dec,
year = "1961",
bibdate = "Tue Jun 21 18:58:31 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
}
@Article{Hosain:1962:NII,
author = "F. Hosain and G. Marsaglia and W. Noyes and C. A.
Finch",
title = "The nature of internal iron exchange in man",
journal = "Transactions of the Association of American
Physicians",
volume = "75",
number = "??",
pages = "59--63",
month = "????",
year = "1962",
ISSN = "0066-9458",
bibdate = "Mon Jun 3 19:13:11 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the Association of American
Physicians",
}
@TechReport{Mann:1962:RC,
author = "H. B. Mann and G. Marsaglia",
title = "A Remark on Circulants",
type = "Mathematical note",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "??",
month = "????",
year = "1962",
bibdate = "Wed Jun 22 06:43:18 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1962:ERB,
author = "George Marsaglia",
title = "Elementary Relations Between Uniform and Normal
Distributions in the Plane",
type = "Report",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "??",
month = aug,
year = "1962",
bibdate = "Wed Nov 12 07:29:32 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0288501",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1962:FPG,
author = "G. Marsaglia and M. D. Maclaren and T. A. Bray",
title = "A Fast Procedure for Generating Normal Random
Variables",
type = "Mathematical note",
number = "282",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
month = aug,
year = "1962",
bibdate = "Tue Jun 21 18:58:31 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=AD0296195",
abstract = "A discussion is given of the generation of normal
random variables very rapidly in a computer --- for
example, at the rate of 10,000--15,000 per second in
the IBM 7090. The method is suitable for any computer.
The incorporation of successive improvements has led to
a procedure which is fairly easy to program, requires
little storage, 300--400 constants, is very fast (it
takes about as long to generate the normal $x$ as the
uniform $u$ from which it comes), and is completely
accurate, in the sense that in theory the procedure
returns a random variable with exactly the required
distribution; in practice the result is an
approximation influenced only by the capacity (word
length) of the computer.",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1962:IPM,
author = "George Marsaglia",
title = "Improving the Polar Method for Generating a Pair of
Normal Random Variables",
type = "Technical report",
number = "D1-82-0203",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
month = sep,
year = "1962",
bibdate = "Wed Nov 12 07:34:34 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0288931",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1962:RVC,
author = "George Marsaglia",
title = "Random Variables and Computers",
type = "Report",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "??",
month = may,
year = "1962",
bibdate = "Wed Nov 12 07:29:32 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0278358",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1962:SPG,
author = "George Marsaglia and T. A. Bray",
title = "A small procedure for generating normal random
variables",
type = "Mathematical note",
number = "283",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "??",
month = nov,
year = "1962",
bibdate = "Wed Jun 22 09:24:42 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
}
@TechReport{MacLaren:1963:FPG,
author = "M. D. MacLaren and G. Marsaglia and T. A. Bray",
title = "A Fast Procedure for Generating Exponential Random
Variables",
type = "Report",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "??",
month = jan,
year = "1963",
bibdate = "Tue Jun 21 18:58:31 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
abstract = "A very fast method for generating exponential random
variables in a digital computer is presented. The
method is exact, in the sense that in theory it returns
a random variable with exactly the exponential
distribution. In practice the result is an
approximation, but the accuracy of the approximation
depends only on the word length of the computer.",
acknowledgement = ack-nhfb,
remark = "Published in \cite{MacLaren:1964:FPG}.",
}
@TechReport{Marsaglia:1963:CER,
author = "George Marsaglia",
title = "The Cumulative Effect of Random Losses in a
Transmission Line",
type = "Mathematical note",
number = "D1-82-0236",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "ii + 14",
month = feb,
year = "1963",
bibdate = "Wed Nov 12 07:42:28 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
note = "Mathematical Note number 289.",
URL = "http://www.dtic.mil/docs/citations/AD0403722;
http://www.dtic.mil/get-tr-doc/pdf?AD=AD0403722",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1963:CMC,
author = "George Marsaglia",
title = "Conditional Means and Covariances of Normal Variables
with Singular Covariance Matrix",
type = "Mathematical note",
number = "288",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
month = feb,
year = "1963",
bibdate = "Tue Jun 21 18:17:38 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0299080",
acknowledgement = ack-nhfb,
remark = "Published in \cite{Marsaglia:1964:CMC}.",
}
@TechReport{Marsaglia:1963:ENDa,
author = "George Marsaglia",
title = "Expressing the Normal Distribution with Covariance
Matrix {$ A + B $} in Terms of One with Covariance
Matrix {$A$}",
type = "Mathematical note",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "??",
month = feb,
year = "1963",
bibdate = "Wed Nov 12 07:42:28 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0299120",
acknowledgement = ack-nhfb,
}
@Article{Marsaglia:1963:ENDb,
author = "George Marsaglia",
title = "Expressing the Normal Distribution with Covariance
Matrix {$ A + B $} in Terms of One with Covariance
Matrix {$A$}",
journal = j-BIOMETRIKA,
volume = "50",
number = "3/4",
pages = "535--538",
month = dec,
year = "1963",
CODEN = "BIOKAX",
DOI = "https://doi.org/10.2307/2333924",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
MRclass = "62.40",
MRnumber = "0181061 (31 \#5290)",
MRreviewer = "I. Olkin",
bibdate = "Sat Jun 21 14:33:13 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315448;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/biometrika1960.bib",
URL = "http://www.jstor.org/stable/2333924",
ZMnumber = "0117.37202",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://biomet.oxfordjournals.org/content/by/year;
http://www.jstor.org/journals/00063444.html",
keywords = "statistics",
}
@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 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
ZMnumber = "0112.08402",
country = "USA",
date = "13/05/93",
descriptors = "RVG",
enum = "7628",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "numerical analysis",
location = "SEL: Wi",
references = "0",
revision = "16/01/94",
}
@TechReport{Marsaglia:1963:GVT,
author = "George Marsaglia",
title = "Generating variables from the tail of the normal
distribution",
type = "Report",
number = "0399324",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "6",
month = sep,
year = "1963",
bibdate = "Wed Jun 22 09:12:52 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0423993;
http://www.stormingmedia.us/39/3993/0399324.html",
acknowledgement = ack-nhfb,
xxtitle = "Generating a Variable from the Tail of the Normal
Distribution",
}
@TechReport{Marsaglia:1963:RNF,
author = "George Marsaglia",
title = "Random numbers fall mainly in the planes",
type = "Report",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "9",
month = aug,
year = "1963",
bibdate = "Wed Nov 12 07:42:28 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.dtic.mil/docs/citations/AD0685578",
abstract = "Most of the world's computer centers use congruential
random number generators. This note points out that
such random number generators produce points in $ 2, 3,
4, \ldots {} $ dimensions which are too regular for
many Monte Carlo calculations. The trouble is that the
points fall exactly on a lattice with quite a gross
structure. The paper gives details of the degree of
regularity of such generators in terms of sets of
relatively few parallel hyperplanes which contain all
of the points produced by the generator.",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1963:SAM,
author = "George Marsaglia",
title = "Stochastic Analysis of Multi-Compartment Systems",
type = "Mathematical note",
number = "313",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "22",
month = jul,
year = "1963",
bibdate = "Tue Jun 21 18:14:31 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
abstract = "This is a discussion of methods for describing,
mathematically, flows between compartments in a
multi-compartment system. We will give the conventional
theory, based on the solution of a system of linear
differential equations; we will also give a theory
based on probability, viewing the system as a
collection of `states' with a particle moving from
state to state with certain probabilities, remaining in
each state a random time with an exponential
distribution. Finally, we will take still another
approach, again based on probability theory, in which
we consider the sojourn time of a particle, that is,
the time it spends after leaving a given compartment
before returning to that compartment.",
acknowledgement = ack-nhfb,
}
@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 (print), 1557-7317 (electronic)",
ISSN-L = "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;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
ZMnumber = "0127.09101",
country = "USA",
date = "13/05/93",
descriptors = "RVG",
enum = "7614",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "numerical analysis; PRNG (pseudo-random number
generator)",
location = "SEL: Wi",
references = "0",
revision = "16/01/94",
}
@TechReport{Marsaglia:1964:BRS,
author = "George Marsaglia",
title = "Bounds for the Rank of the Sum of Two Matrices",
type = "Report",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "13",
month = apr,
year = "1964",
bibdate = "Wed Nov 12 07:42:28 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0600471",
acknowledgement = ack-nhfb,
}
@Article{Marsaglia:1964:CMC,
author = "George Marsaglia",
title = "Conditional Means and Covariances of Normal Variables
with Singular Covariance Matrix",
journal = j-J-AM-STAT-ASSOC,
volume = "59",
number = "308",
pages = "1203--1204",
month = dec,
year = "1964",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:37 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314189;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1960.bib",
URL = "http://www.jstor.org/stable/2282635",
ZMnumber = "0124.11303",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "statistics",
}
@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",
month = "????",
year = "1964",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1006063",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65.15",
MRnumber = "30 \#2660",
MRreviewer = "D. H. Lehmer",
bibdate = "Thu Mar 27 09:05:15 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/6/3;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://www.jstor.org/stable/2027592",
ZMnumber = "0125.08001",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1964",
}
@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",
DOI = "https://doi.org/10.1145/363872.363883",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:51 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
ZMnumber = "0127.09005",
acknowledgement = ack-nhfb,
country = "USA",
date = "13/05/93",
descriptors = "RVG",
enum = "7637",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "numerical analysis; PRNG (pseudo-random number
generator)",
location = "SEL: Wi",
references = "0",
revision = "16/01/94",
}
@Article{Marsaglia:1964:GVT,
author = "George Marsaglia",
title = "Generating a Variable from the Tail of the Normal
Distribution",
journal = j-TECHNOMETRICS,
volume = "6",
number = "1",
pages = "101--102",
month = feb,
year = "1964",
CODEN = "TCMTA2",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Wed Jun 22 09:29:50 2011",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.jstor.org/stable/1266749",
acknowledgement = ack-nhfb,
date = "13/05/93",
descriptors = "RVG",
enum = "7629",
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html;
http://www.tandfonline.com/loi/utch20",
location = "SEL: Wi",
references = "0",
revision = "16/01/94",
}
@TechReport{Marsaglia:1964:MCR,
author = "George Marsaglia and Albert W. Marshall and Frank
Proschan",
title = "Moment Crossings as Related to Density Crossings",
type = "Report",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "??",
month = jul,
year = "1964",
bibdate = "Wed Nov 12 07:42:28 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0603582",
abstract = "In this paper it is shown how the number of moment
crossings of two symmetrical densities is related to
the number of crossings of the densities. This
generalizes a result of Fisher's recently proved by
Finucan (1964) (A note on Kurtosis).",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1964:MPR,
author = "George Marsaglia",
title = "A Method for Producing Random Variables in a
Computer",
type = "Mathematical note",
number = "342",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "13",
month = feb,
year = "1964",
bibdate = "Tue Jun 21 18:14:31 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0601118",
abstract = "This paper describes a general procedure for producing
random variables in a computer. The idea is to
represent the required $X$ in the form: $ X = C (M +
U_1 + U_2 + U_3) $, some 97--99\% of the time, where c
is constant, $M$ is a discrete random variable taking
perhaps $8$ values, and the $U$'s are uniform random
variables; the other 1--3\% of the time, $X$ is
generated from a residual density by the rejection
technique. These two methods for producing $X$ are
combined in the proper proportions in order that the
resulting distribution for $X$ be correct. The method
is general in that it applies to a wide variety of
density functions. Programs based on this procedure are
very fast and require little computer storage space ---
typically, 18 constants and 20 instructions.",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1964:RDA,
author = "George Marsaglia",
title = "The Radiation Dose Accumulated by Blood Diverted
Through a Shunt",
type = "Mathematical note",
number = "357",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "8",
month = jul,
year = "1964",
bibdate = "Tue Jun 21 19:32:04 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
abstract = "Modern techniques have made it possible to divert a
portion of the circulating blood through a shunt
outside the body --- for example in heart-lung
machines, artificial kidneys, and coiled tubes where
the blood may be exposed to radiation without danger to
body tissues. There is some probability theory
connected with such procedures, for the cells of the
blood are thoroughly mixed in the body, and hence the
number of times a blood cell passes through the shunt
is a random variable. Several papers have been written
to describe such systems by differential equations;
this paper discusses the problem directly in terms of
probability theory, finding the exact distribution of
the number of times a blood cell has passed through the
shunt and, in addition, a normal approximation which
makes calculation of accumulated doses a matter of
simple arithmetic.",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1964:RNV,
author = "George Marsaglia",
title = "Ratios of normal variables and ratios of sums of
variables",
type = "Mathematical note",
number = "D1-82-0348",
institution = "Mathematics Research Laboratory, Boeing Scientific
Research Laboratories",
address = "Seattle, WA, USA",
pages = "iii + 13 + 3",
month = apr,
year = "1964",
bibdate = "Wed Nov 12 07:14:08 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0600972;
http://www.dtic.mil/dtic/tr/fulltext/u2/600972.pdf;
http://www.dtic.mil/get-tr-doc/pdf?AD=AD0600972",
abstract = "The principal part of this paper is devoted to the
study of the distribution and density functions of the
ratio of two normal random variables. It gives several
representations of the distribution function in terms
of the bivariate normal distribution and Nicholson's
$V$ function, both of which have been extensively
studied, and for which tables and computational
procedures are readily available. One of these
representations leads to an easy derivation of the
density function in terms of the Cauchy density and the
normal density and integral. A number of graphs of the
possible shapes of the density are given, together with
an indication of when the density is unimodal or
bimodal.\par
The last part of the paper discusses the distribution
of the ratio $ (u_1 + \cdots + u_n) / (v_1 + \cdots +
v_m)$ where the $u$'s and $v$'s are, independent,
uniform variables. The distribution for all $n$ and $m$
is given, and some approximations discussed.",
acknowledgement = ack-nhfb,
remark = "Published in \cite{Marsaglia:1965:RNV}.",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
ZMnumber = "0123.36205",
keywords = "probability theory",
}
@TechReport{Marsaglia:1964:SPIa,
author = "George Marsaglia",
title = "Some Problems Involving Circular and Spherical
Targets",
type = "Report",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "19",
month = apr,
year = "1964",
bibdate = "Wed Nov 12 07:42:28 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.dtic.mil/docs/citations/AD0600566",
abstract = "This article is concerned with some problems which
occur in certain tactical considerations: how should
one place $k$ circles (spheres) in the plane (3-space)
so that their union has the greatest standard normal
probability measure, that is, so as to maximize the
probability that a random normal point will fall in one
or more of the circles (spheres). For $ k > 3$ the
problem seems hopeless, (except for certain special
situations); the case for $ k = 3$ is still unresolved
and is being worked on by a number of investigators,
and the case for $ k = 2$ is solved completely in this
paper. The results for $ k = 2$ have some practical
value when applied to actual problems arising in
tactical considerations, and some theoretical value, as
a method of attacking the problem for $ k > 3$.",
acknowledgement = ack-nhfb,
}
@Article{Marsaglia:1964:SPIb,
author = "George Marsaglia",
title = "Some Problems Involving Circular and Spherical
Targets",
journal = j-OPER-RES,
volume = "13",
number = "1",
pages = "18--27",
month = jan # "\slash " # feb,
year = "1964",
CODEN = "OPREAI",
DOI = "https://doi.org/10.1287/opre.13.1.18",
ISSN = "0030-364X (print), 1526-5463 (electronic)",
ISSN-L = "0030-364X",
bibdate = "Tue Jun 21 18:50:19 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.jstor.org/stable/167951",
abstract = "This article is concerned with some problems that
occur in certain tactical considerations: how should
one place $k$ circles [spheres] in the plane [3-space]
so that their union has the greatest standard normal
probability measure, that is, so as to maximize the
probability that a random normal point will fall in one
or more of the circles [spheres]. For $ k > 3 $ the
problem seems hopeless, (except for certain special
situations); the case for $ k = 3 $ is still unresolved
and is being worked on by a number of investigators,
and the case for $ k = 2 $ is solved completely in this
paper. The results for $ k = 2 $ have some practical
value when applied to actual problems arising in
tactical considerations, and some theoretical value, as
a method of attacking the problem for $ k \geq 3 $.",
acknowledgement = ack-nhfb,
fjournal = "Operations Research",
journal-URL = "http://pubsonline.informs.org/loi/opre",
}
@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",
DOI = "https://doi.org/10.1145/321250.321257",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65.15",
MRnumber = "30 \#687",
bibdate = "Mon Jan 22 17:05:44 MST 2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jacm.bib;
MathSciNet database",
ZMnumber = "0143.40101",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "numerical analysis",
oldlabel = "MacLarenM65",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/jacm/MacLarenM65",
}
@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",
number = "5",
pages = "443--450",
month = nov,
year = "1965",
CODEN = "JFINAB",
DOI = "https://doi.org/10.1016/0016-0032(65)90533-8",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
bibdate = "Wed Nov 12 14:50:37 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
ZMnumber = "0173.21401",
acknowledgement = ack-nhfb,
fjournal = "Journal of {The Franklin Institute}",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
keywords = "information, communication",
}
@Article{Marsaglia:1965:CNS,
author = "George Marsaglia",
title = "Classroom Notes: Short Proof of a Result on
Determinants",
journal = j-AMER-MATH-MONTHLY,
volume = "72",
number = "2",
pages = "173--173",
month = feb,
year = "1965",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Thu Jul 8 18:23:41 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Article{Marsaglia:1965:DRD,
author = "G. Marsaglia and E. D. Thomas",
title = "Distribution of radiation dose accumulated by blood
during extracorporeal irradiation",
journal = j-RADIAT-RES,
volume = "??",
number = "??",
pages = "??--??",
month = "????",
year = "1965",
CODEN = "RAREAE",
ISSN = "0033-7587 (print), 1938-5404 (electronic)",
ISSN-L = "0033-7587",
bibdate = "Wed Jun 22 08:14:28 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
fjournal = "Radiation Research",
journal-URL = "http://www.jstor.org/journal/radirese",
remark = "Cited as in press in \cite{Thomas:1965:TLE}.",
}
@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",
number = "1",
pages = "91--93",
month = jan,
year = "1965",
CODEN = "JSTBAJ",
ISSN = "0035-9246",
MRclass = "60.20",
MRnumber = "32 \#6514",
MRreviewer = "D. R. Barr",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
ZMnumber = "0128.38905",
fjournal = "Journal of the Royal Statistical Society. Series B
(Methodological)",
journal-URL = "http://www.jstor.org/journals/00359246.html",
keywords = "statistics",
}
@Article{Marsaglia:1965:RDA,
author = "George Marsaglia and E. Donnall Thomas",
title = "The Radiation Dose Accumulated by Blood during
Extracorporeal Irradiation",
journal = j-RADIAT-RES,
volume = "25",
number = "2",
pages = "269--276",
month = jun,
year = "1965",
CODEN = "RAREAE",
DOI = "https://doi.org/10.2307/3571970",
ISSN = "0033-7587 (print), 1938-5404 (electronic)",
ISSN-L = "0033-7587",
bibdate = "Tue Jun 21 18:30:35 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.jstor.org/stable/3571970",
acknowledgement = ack-nhfb,
ajournal = "Radiat. Res.",
fjournal = "Radiation Research",
journal-URL = "http://www.jstor.org/journal/radirese",
}
@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",
number = "309",
pages = "193--204",
month = mar,
year = "1965",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "60.20",
MRnumber = "31 \#2747",
MRreviewer = "S. R. Searle",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
URL = "http://www.jstor.org/stable/2283145",
ZMnumber = "0126.35302",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "statistics",
}
@TechReport{Marsaglia:1965:SAM,
author = "George Marsaglia",
title = "Still Another Method for Producing Normal Variables in
a Computer",
type = "Mathematical note",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "8",
month = jan,
year = "1965",
bibdate = "Tue Jun 21 18:58:31 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0612430",
abstract = "A method for producing normal random variables in
terms of uniform random variables $ U_1, U_2, U_3,
\ldots {} $. If $ Y = U_1 + U_2 + U_3 $, then choosing
one of the four random variables $ 2 Y - 3 $, $ (4 Y -
6) / 3 $, $ (Y - 7) / 2 $ or $ (Y + 4) / 2 $ in the
proportions $ 0.8365 $, $ 0.11506 $, $ 0.00372 $ and $
0.00372 $ will produce the required normal variate $
98.6 $ percent of the time. The other $ 1.4 $ percent
is devoted to the tail or a rejection technique in
order that the composite be exact. The method leads to
very fast computer programs which are easy to code and
occupy little space in the computer.",
acknowledgement = ack-nhfb,
}
@Article{Marsaglia:1965:SPI,
author = "George Marsaglia",
title = "Some Problems Involving Circular and Spherical
Targets",
journal = j-OPER-RES,
volume = "13",
number = "1",
pages = "18--27",
month = jan # "\slash " # feb,
year = "1965",
CODEN = "OPREAI",
DOI = "https://doi.org/10.1287/opre.13.1.18",
ISSN = "0030-364X (print), 1526-5463 (electronic)",
ISSN-L = "0030-364X",
bibdate = "Wed Nov 12 10:07:25 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://pubsonline.informs.org/doi/pdf/10.1287/opre.13.1.18",
acknowledgement = ack-nhfb,
fjournal = "Operations Research",
journal-URL = "http://pubsonline.informs.org/loi/opre",
}
@Article{Thomas:1965:TLE,
author = "E. D. Thomas and R. B. Epstein and J. W. {Eschbach
Jr.} and D. Prager and C. D. Buckner and G. Marsaglia",
title = "Treatment of Leukemia by Extracorporeal Irradiation",
journal = j-NEW-ENGLAND-J-MED,
volume = "273",
number = "1",
pages = "6--12",
day = "1",
month = jul,
year = "1965",
CODEN = "NEJMAG",
DOI = "https://doi.org/10.1056/NEJM196507012730102",
ISSN = "0028-4793 (print), 1533-4406 (electronic)",
ISSN-L = "0028-4793",
bibdate = "Tue Jun 21 18:20:14 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.ncbi.nlm.nih.gov/pubmed/14297099;
http://www.nejm.org/doi/full/10.1056/NEJM196507012730102",
acknowledgement = ack-nhfb,
ajournal = "N. Engl. J. Med.",
fjournal = "The New England Journal of Medicine",
journal-URL = "http://www.nejm.org/medical-index",
}
@InProceedings{Marsaglia:1966:GMP,
author = "G. Marsaglia",
booktitle = "Proceedings of the Fall Joint Computer Conference, San
Francisco, November 1966",
title = "A general method for producing random variables in a
computer",
publisher = "Spartan Books",
address = "Washington, DC, USA",
bookpages = "vii + 819",
pages = "169--173",
year = "1966",
LCCN = "TK7885.A1 J74 1966 Fall",
bibdate = "Fri Jan 6 09:58:50 2012",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
acknowledgement = ack-nhfb,
country = "USA",
date = "13/05/93",
descriptors = "RVG",
enum = "7631",
location = "SEL: Wi",
references = "0",
revision = "16/01/94",
town = "San Francisco",
}
@Article{Hosain:1967:BFN,
author = "Fazle Hosain and George Marsaglia and Clement A.
Finch",
title = "Blood Ferrokinetics in Normal Man",
journal = j-J-CLIN-INVEST,
volume = "46",
number = "1",
pages = "1--9",
month = jan,
year = "1967",
CODEN = "JCINAO",
DOI = "https://doi.org/10.1172/JCI105501",
ISSN = "0021-9738 (print), 1558-8238 (electronic)",
ISSN-L = "0021-9738",
bibdate = "Tue Jun 21 18:09:18 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC297014/",
acknowledgement = ack-nhfb,
ajournal = "J. Clin. Invest.",
fjournal = "Journal of Clinical Investigation",
journal-URL = "http://www.jci.org/archive",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
}
@TechReport{Marsaglia:1967:ORF,
author = "George Marsaglia",
title = "Optimal Representation of a Function as a Linear
Combination of Functions",
type = "Report",
number = "0841156",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "14",
month = mar,
year = "1967",
bibdate = "Wed Jun 22 06:38:08 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0651148;
http://www.stormingmedia.us/84/8411/0841156.html",
abstract = "This paper discusses the approximation of a given
density function g(x) with a linear combination of
densities $ f_1 (x), f_2 (x), \ldots {}, f_n(x) $ in
such a way that the approximation has maximum area but
always lies below the given function.",
acknowledgement = ack-nhfb,
}
@Article{Morgan:1967:MII,
author = "E. H. Morgan and G. Marsaglia and E. R. Giblett and C.
A. Finch",
title = "A method of investigating internal iron exchange
utilizing two types of transferrin",
journal = j-J-LAB-CLIN-MED,
volume = "63",
number = "3",
pages = "370--381",
month = mar,
year = "1967",
CODEN = "JLCMAK",
ISSN = "0022-2143 (print), 1532-6543 (electronic)",
ISSN-L = "0022-2143",
bibdate = "Tue Jun 21 18:26:32 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Lab. Clin. Med.",
fjournal = "Journal of Laboratory and Clinical Medicine",
}
@TechReport{Marsaglia:1968:OLRa,
author = "George Marsaglia and T. A. Bray",
title = "One-line random number generators and their use in
combinations",
type = "Report",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "12",
month = mar,
year = "1968",
bibdate = "Wed Nov 12 07:42:28 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0667956",
abstract = "This is a discussion of some one-line random number
generators, requiring a single FORTRAN instruction,
together with a description of some short FORTRAN
programs which mix several such generators. Evidence
suggesting that the simple congruential generators are
unsatisfactory continues to grow; one of the most
promising alternatives is to mix several simple
generators. These composite generators do better in
various tests for randomness than do the simple
congruential generators used at many computer
centers.",
acknowledgement = ack-nhfb,
}
@Article{Marsaglia:1968:OLRb,
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 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.15",
MRnumber = "39\#5040",
MRreviewer = "R. R. Coveyou",
bibdate = "Fri Nov 25 18:20:22 MST 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
MathSciNet database",
ZMnumber = "0164.18802",
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",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "FORTRAN; Monte Carlo; numerical analysis; PRNG
(pseudo-random number generator); random number
generation; simulation; utility programs",
ZMreviewer = "R. R. Coveyou",
}
@Article{Marsaglia:1968:QPR,
author = "George Marsaglia",
title = "Query 27: Pseudo Random Normal Numbers",
journal = j-TECHNOMETRICS,
volume = "10",
number = "2",
pages = "401--402",
month = may,
year = "1968",
CODEN = "TCMTA2",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Sat Mar 03 08:18:20 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.jstor.org/stable/1267057",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html;
http://www.tandfonline.com/loi/utch20",
}
@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",
DOI = "https://doi.org/10.1073/pnas.61.1.25",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
MRclass = "65.15",
MRnumber = "38 \#3998",
MRreviewer = "R. R. Coveyou",
bibdate = "Thu Nov 14 11:39:48 2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.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}.",
ZMnumber = "0172.21002",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
keywords = "numerical analysis; PRNG (pseudo-random number
generator)",
}
@TechReport{Marsaglia:1969:OSA,
author = "George Marsaglia",
title = "One-Sided Approximations by Linear Combinations of
Functions",
type = "Report",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "18",
month = sep,
year = "1969",
bibdate = "Wed Nov 12 07:42:28 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0695796",
abstract = "The paper discusses how to approximate a function $
g(x) $ from one side by a linear combination of
functions $ f_1 (x), \ldots {}, f_n(x) $ so as to
minimize the area between the two. It discusses the
problem as one of finding the point where a moving
hyperplane last touches a convex set and an approximate
procedure based on linear programming methods. It gives
details of an algorithm for solving the problem,
examples, and applications to Monte Carlo Theory ---
generating random variables in a computer.",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:1969:RCR,
author = "George Marsaglia",
title = "Regularities in congruential random number
generators",
type = "Report",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "8",
month = may,
year = "1969",
bibdate = "Wed Nov 12 07:42:28 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0689295",
abstract = "The paper suggests that points in $n$-space produced
by congruential random number generators are too
regular for general Monte Carlo use. Regularity was
established previously for multiplicative congruential
generators by showing that all the points fall in sets
of relatively few parallel hyperplanes. The existence
of many containing sets of parallel hyperplanes was
easily established, but proof that the number of
hyperplanes was small required a result of Minkowski
from the geometry of numbers --- a symmetric, convex
set of volume 2 to the nth power must contain at least
two points with integral coordinates. The present paper
takes a different approach to establishing the course
lattice structure of congruential generators. It gives
a simple, self-contained proof that points in $n$-space
produced by the general congruential generator $ r_(i +
1)$ is identically equal to $ a(r_i) + b \bmod m$ must
fall on a lattice with unit-cell volume at least $m$ to
the power $ (n - 1)$. There is no restriction on $a$ or
$b$; this means that all congruential random number
generators must be considered unsatisfactory in terms
of lattices containing the points they produce, for a
good generator of random integers should have an
$n$-lattice with unit-cell volume 1.",
acknowledgement = ack-nhfb,
}
@Article{Cook:1970:FBM,
author = "J. D. Cook and G. Marsaglia and J. W. Eschbach and D.
D. Funk and C. A. Finch",
title = "Ferrokinetics: a biologic model for plasma iron
exchange in man",
journal = j-J-CLIN-INVEST,
volume = "49",
number = "2",
pages = "197--205",
month = feb,
year = "1970",
CODEN = "JCINAO",
DOI = "https://doi.org/10.1172/JCI106228",
ISSN = "0021-9738 (print), 1558-8238 (electronic)",
ISSN-L = "0021-9738",
bibdate = "Tue Jun 21 18:11:41 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC322461/;
http://www.pubmedcentral.gov/articlerender.fcgi?artid=322461",
acknowledgement = ack-nhfb,
ajournal = "J. Clin. Invest.",
fjournal = "Journal of Clinical Investigation",
journal-URL = "http://www.jci.org/archive",
}
@Article{Finch:1970:FM,
author = "C. A. Finch and K. Deubelbeiss and J. D. Cook and J.
W. Eschbach and L. A. Barker and D. D. Funk and G.
Marsaglia and R. S. Hillman and S. Slichter and J. W.
Adamson and A. Ganzoni and E. R. Giblett",
title = "Ferrokinetics in Man",
journal = j-MEDICINE,
volume = "49",
number = "1",
pages = "17--54",
month = jan,
year = "1970",
CODEN = "MEDIAV",
ISSN = "0025-7974 (print), 1536-5964 (electronic)",
ISSN-L = "0025-7974",
bibdate = "Tue Jun 21 18:03:38 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://journals.lww.com/md-journal/Citation/1970/01000/Ferrokinetics_in_Man.2.aspx",
acknowledgement = ack-nhfb,
fjournal = "Medicine (Baltimore)",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
ZMnumber = "0246.90027",
ZMclass = "*90-04 Machine computation, programs (optimization)
90C05 Linear programming 41A50 Best approximation",
}
@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)",
ISSN-L = "0029-599X",
MRclass = "65.15",
MRnumber = "42 \#8651",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/nummath.bib;
MathSciNet database",
ZMnumber = "0212.18204",
acknowledgement = ack-nhfb,
classification = "C7890 (Other special applications of computing)",
corpsource = "Boeing Sci. Res. Labs., Seattle, WA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "random number generation",
xxyear = "1970/1971",
ZMclass = "*65C10 Random number generation",
}
@TechReport{Marsaglia:1970:RVI,
author = "George Marsaglia",
title = "Random Variables with Independent Binary Digits",
type = "Report",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
pages = "15",
month = jan,
year = "1970",
bibdate = "Wed Nov 12 07:42:28 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.dtic.mil/docs/citations/AD0705642",
abstract = "Let $ X = .b_1 b_2 b_3 \ldots {} $ be a random
variable with independent binary digits $ b_n $ taking
values $0$ or $1$ with probabilities $ p_n$ and $ q_n$.
When does $X$ have a density function? A continuous
density function? A singular distribution? This note
proves that the distribution $X$ is singular is and
only if the tail of the series $ \sum (\log (p_n /
q_n))$ squared diverges, and that $X$ has a density
that is positive on some interval if and only if $ \log
(p_n / q_n)$ is a geometric sequence with ratio $ 1 /
2$ for $n$ greater than some $k$, and in that case the
fractional part of $ 2^k X$ has an exponential density
(increasing or decreasing with the uniform density a
special case). It gives a sufficient condition for $X$
to have a density, ($ \sum \log (2 \max (p_n, q_n))$
converges), but unless the tail of the sequence $ \log
(p_n / q_n)$ is geometric, ratio $ 1 / 2$, the density
is a weird one that vanishes at least once in every
interval.",
acknowledgement = ack-nhfb,
}
@Article{Marsaglia:1971:MCC,
author = "George Marsaglia and E. D. Thomas",
title = "Mathematical Consideration of Cross Circulation and
Exchange",
journal = j-TRANSFUSION,
volume = "11",
number = "4",
pages = "216--219",
month = jul # "\slash " # aug,
year = "1971",
CODEN = "TRANAT",
DOI = "https://doi.org/10.1111/j.1537-2995.1971.tb04404.x",
ISSN = "0041-1132 (print), 1537-2995 (electronic)",
ISSN-L = "0041-1132",
bibdate = "Sat Jun 11 09:46:51 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
abstract = "Equations are presented that describe the kinetics of
cross circulation and of exchange transfusion. These
equations should be useful in calculating the movement
of cells and metabolic substances between vascular and
extravascular compartments.",
acknowledgement = ack-nhfb,
fjournal = "Transfusion (Bethesda)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1537-2995",
}
@Article{Marsaglia:1971:RVI,
author = "George Marsaglia",
title = "Random variables with independent binary digits",
journal = j-ANN-MATH-STAT,
volume = "42",
number = "6",
pages = "1922--1929",
month = dec,
year = "1971",
CODEN = "AASTAD",
DOI = "https://doi.org/10.1214/aoms/1177693058",
ISSN = "0003-4851",
MRclass = "60A05",
MRnumber = "45 \#7764",
MRreviewer = "A. Fuchs",
bibdate = "Fri Jan 6 09:58:57 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
MathSciNet database",
URL = "http://projecteuclid.org/euclid.aoms/1177693058;
http://www.jstor.org/stable/2240118",
ZMnumber = "0239.60015",
abstract = "Let $ X = \cdot b_1 b_2 b_3 \cdots $ be a random
variable with independent binary digits $ b_n $ taking
values 0 or 1 with probability $ p_n $ and $ q_n = 1 -
p_n $. When does $X$ have a density? A continuous
density? A singular distribution? This note gives
necessary and sufficient conditions for the
distribution of $X$ to be: discrete: $ \Sigma \min
(p_n, q_n) < \infty $; singular: $ \Sigma^\infty_m
\lbrack \log (p_n / q_n) \rbrack^2 = \infty $ for every
$m$; absolutely continuous: $ \Sigma^\infty_m \lbrack
\log (p_n / q_n) \rbrack^2 < \infty $ for some $m$.
Furthermore, $X$ has a density that is bounded away
from zero on some interval if and only if $ \log (p_n /
q_n) $ is a geometric sequence with ratio $ \frac
{1}{2} $ for $ n > k $, and in that case the fractional
part of $ 2^k X $ has an exponential density
(increasing or decreasing with the uniform a special
case).",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
ZMclass = "60E05 General theory of probability distributions
60F99 Limit theorems (probability)",
}
@Article{Marsaglia:1972:CPS,
author = "George Marsaglia",
title = "Choosing a point from the surface of a sphere",
journal = j-ANN-MATH-STAT,
volume = "43",
number = "2",
pages = "645--646",
month = apr,
year = "1972",
CODEN = "AASTAD",
DOI = "https://doi.org/10.1214/aoms/1177692644",
ISSN = "0003-4851",
MRclass = "65C10",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://projecteuclid.org/euclid.aoms/1177692644;
http://www.jstor.org/stable/2240001",
ZMnumber = "0248.65008",
fjournal = "Annals of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
ZMclass = "*65C10 Random number generation",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
ZMnumber = "0266.65007",
acknowledgement = ack-nhfb,
ZMclass = "*65C10 Random number generation",
}
@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",
number = "3",
pages = "451--452",
month = "????",
year = "1972",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1972-082-8",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "15A03",
MRnumber = "47 \#236",
MRreviewer = "A. R. Amir-Moez",
bibdate = "Thu Sep 8 10:04:00 MDT 2011",
bibsource = "http://cms.math.ca/cmb/v15/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
ZMnumber = "0252.15002",
acknowledgement = ack-nhfb,
fjournal = "Canadian mathematical bulletin = Bulletin canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
ZMclass = "*15A03 Vector spaces",
}
@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",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
}
@Article{Marsaglia:1974:APRa,
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",
number = "4",
pages = "747--747",
month = aug,
year = "1974",
CODEN = "APBYAE",
DOI = "https://doi.org/10.1214/aop/1176996619",
ISSN = "0091-1798",
ISSN-L = "0091-1798",
MRclass = "60A05",
MRnumber = "49 \#8070",
bibdate = "Sun Apr 20 10:44:17 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/annprobab1970.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
MathSciNet database",
URL = "http://projecteuclid.org/euclid.aop/1176996619",
ZMnumber = "0284.60018",
acknowledgement = ack-nhfb,
fjournal = "Annals of Probability",
journal-URL = "http://projecteuclid.org/all/euclid.aop",
ZMclass = "60E05 General theory of probability distributions
60F99 Limit theorems (probability)",
}
@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-STAT,
volume = "2",
number = "4",
pages = "848--848",
year = "1974",
CODEN = "ASTSC7",
DOI = "https://doi.org/10.1214/aos/1176342776",
ISSN = "0090-5364",
MRclass = "60A10",
MRnumber = "50 \#1310",
MRreviewer = "A. Fuchs",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
URL = "http://projecteuclid.org/euclid.aos/1176342776",
ZMnumber = "0284.60017",
fjournal = "Annals of Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aos/",
ZMclass = "*60E05 General theory of probability distributions
60F99 Limit theorems (probability)",
}
@Article{Marsaglia:1974:EIR,
author = "George Marsaglia and George P. H. Styan",
title = "Equalities and Inequalities for Ranks of Matrices",
journal = j-LIN-AND-MULT-ALGEBRA,
volume = "2",
number = "3",
pages = "269--292",
year = "1974",
CODEN = "LNMLAZ",
DOI = "https://doi.org/10.1080/03081087408817070",
ISSN = "0308-1087 (print), 1563-5139 (electronic)",
ISSN-L = "0308-1087",
MRclass = "15A45",
MRnumber = "52 \#5711",
MRreviewer = "A. R. Amir-Moez",
bibdate = "Tue Sep 20 15:09:41 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/linmultalgebra.bib;
MathSciNet database",
ZMnumber = "0297.15003",
acknowledgement = ack-nhfb,
fjournal = "Linear and Multilinear Algebra",
journal-URL = "http://www.tandfonline.com/loi/glma20",
onlinedate = "03 Apr 2008",
ZMclass = "*15A03 Vector spaces 15A39 Linear inequalities 15A45
Miscellaneous inequalities involving matrices",
}
@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",
month = "10",
year = "1974",
CODEN = "SANABS",
ISSN = "0036-4452",
MRclass = "15A09",
MRnumber = "52 \#5699",
MRreviewer = "Thomas L. Boullion",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
ZMnumber = "0309.15002",
fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series A.
Methods and Techniques",
ZMclass = "*15A09 Matrix inversion 15A03 Vector spaces",
}
@Article{Fillet:1975:IHI,
author = "G. Fillet and G. Marsaglia",
title = "Idiopathic Hemochromatosis ({IH}) --- Abnormality in
{RBC} Transport of Iron by Reticuloendothelial System
({RES})",
journal = j-BLOOD,
volume = "46",
number = "6",
pages = "1007--1007",
month = "????",
year = "1975",
CODEN = "BLOOAW",
ISSN = "0006-4971 (print), 1528-0020 (electronic)",
ISSN-L = "0006-4971",
bibdate = "Mon Jun 3 19:13:11 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
fjournal = "Blood",
}
@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 = "http://www.math.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",
number = "2",
pages = "353--354",
month = apr,
year = "1975",
CODEN = "APBYAE",
DOI = "https://doi.org/10.1214/aop/1176996406",
ISSN = "0091-1798",
ISSN-L = "0091-1798",
MRclass = "62E10",
MRnumber = "51 \#2073",
MRreviewer = "Ramesh C. Gupta",
bibdate = "Sun Apr 20 10:44:17 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/annprobab1970.bib;
MathSciNet database",
URL = "http://projecteuclid.org/euclid.aop/1176996406",
ZMnumber = "0336.60017",
abstract = "The exponential distribution is often characterized as
the only distribution with lack of memory. This note
points out a stronger result: the exponential is the
only distribution that is occasionally forgetful.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Probability",
journal-URL = "http://projecteuclid.org/all/euclid.aop",
ZMclass = "*60E05 General theory of probability distributions
62E10 Structure theory of statistical distributions",
}
@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 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "65C10",
MRnumber = "55 \#11560",
MRreviewer = "I. Vaduva",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/ipl/ipl5.html#MarsagliaAP76;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/infoproc1970.bib;
MathSciNet database",
ZMnumber = "0332.65003",
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",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
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",
}
@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 = "http://www.math.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-COMPUT-MATH-APPL,
volume = "3",
number = "4",
pages = "321--325",
year = "1977",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(77)90089-X",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65C10",
MRnumber = "58 \#13613",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
ZMnumber = "0384.65005",
abstract = "This paper describes an exact method for computer
generation of random variables with a gamma
distribution. The method is based on the
Wilson--Hilferty transformation and an improvement on
the rejection technique. The idea is to ``squeeze'' a
target density between two functions, the top one easy
to sample from, the bottom one easy to evaluate.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
ZMclass = "*65C10 Random number generation 60E05 General theory
of probability distributions",
}
@Article{Skarberg:1978:PRK,
author = "Karl Skarberg and Mary Eng and Helmut Huebers and
George Marsaglia and Clement Finch",
title = "Plasma radioiron kinetics in man: explanation for the
effect of plasma iron concentration",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "75",
number = "3",
pages = "1559--1561",
month = mar,
year = "1978",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.75.3.1559",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Sat Jun 11 00:56:04 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.pnas.org/content/75/3/1559.short;
http://www.pubmedcentral.gov/articlerender.fcgi?artid=411513",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
}
@Article{Marsaglia:1980:CGN,
author = "George Marsaglia and I. J. Good",
title = "{C69}. {Generating} a normal sample with given sample
mean and variance",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "11",
number = "1",
pages = "71--74",
year = "1980",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949658008810390",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Tue Apr 22 09:10:47 MDT 2014",
bibsource = "http://jscs.stat.vt.edu/JSCS/articles/v11n1.html;
http://jscs.statjournals.net/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib;
http://www.tandf.co.uk/journals/titles/00949655.html;
Science Citation Index",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
}
@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",
DOI = "https://doi.org/10.2307/2006231",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65C10",
MRnumber = "81a:65015",
bibsource = "Distributed/QLD.bib; Distributed/QLD/1980.bib;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database; MathSciNet database",
ZMnumber = "0423.65005",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "algorithm; t-distribution",
ZMclass = "*65C10 Random number generation 65C05 Monte Carlo
methods",
}
@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 = "http://www.math.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",
CODEN = "????",
ISSN = "0453-8382",
bibdate = "Fri Jan 6 09:50:41 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
ZMnumber = "0535.60013",
abstract = "Translation from Ann. Math. Stat. 42, 1922--1929
(1971; Zbl 0239.60015).",
acknowledgement = ack-nhfb,
fjournal = "Kiberneti{\v{c}}eskij sbornik. Novaya Seriya",
fjournal-2 = "Kiberneti{\c{c}}eskij sbornik (KS): sbornik statej",
keywords = "independent binary digits",
language = "Russian",
ZMclass = "*60E05 General theory of probability distributions
60F99 Limit theorems (probability)",
}
@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",
month = mar,
year = "1984",
CODEN = "JSTNAL",
DOI = "https://doi.org/10.2307/2288360",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "65C10",
MRnumber = "85d:65010",
bibdate = "Mon May 5 12:36:01 MDT 1997",
bibsource = "Distributed/QLD.bib; Distributed/QLD/1984.bib;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
MathSciNet database",
URL = "http://www.jstor.org/stable/2288360",
ZMnumber = "0552.65005",
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.",
acknowledgement = ack-nhfb,
country = "USA",
date = "13/05/93",
descriptors = "RVG",
enum = "7634",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "gamma-and t-variates; inverse of a probability
distribution",
location = "SEL: Wi",
revision = "16/01/94",
ZMclass = "*65C10 Random number generation 65C05 Monte Carlo
methods",
}
@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",
DOI = "https://doi.org/10.1137/0905026",
ISSN = "0196-5204",
MRclass = "65U05 (65C10)",
MRnumber = "86a:65137",
MRreviewer = "Mervin Muller",
bibdate = "Tue Apr 29 19:18:28 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/fortran2.bib;
http://www.math.utah.edu/pub/tex/bib/matlab.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib;
MathSciNet database",
ZMnumber = "0573.65116",
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",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
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",
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",
DOI = "https://doi.org/10.1137/0905034",
ISSN = "0196-5204",
MRclass = "65C10 (62H99)",
MRnumber = "85h:65018",
MRreviewer = "G. P. Bhattacharjee",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib;
MathSciNet database",
ZMnumber = "0552.65006",
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",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
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",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://stat.fsu.edu/pub/diehard/;
http://www.evensen.org/marsaglia/keynote.ps",
acknowledgement = ack-nhfb,
remark = "This paper introduces the Parking Lot test used in the
Diehard Battery test suite.",
}
@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",
DOI = "https://doi.org/10.1016/0024-3795(85)90192-2",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65C10 (15A99)",
MRnumber = "86g:65018",
MRreviewer = "Gheorghe Barbu",
bibdate = "Thu Jan 23 11:18:08 MST 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
ZMnumber = "0572.65002",
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",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "lagged Fibonacci; maximal period; randomness;
shift-register",
ZMclass = "*65C10 Random number generation",
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 = "C-34",
number = "8",
pages = "756--758",
month = aug,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676623",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65C10",
MRnumber = "86h:65010",
bibdate = "Sun Jul 10 08:33:24 MDT 2011",
bibsource = "http://dblp.uni-trier.de/db/journals/tc/tc34.html#Marsaglia85;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib;
MathSciNet database",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676623",
ZMnumber = "0572.65001",
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.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
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",
ZMreviewer = "K. Uosaki",
}
@Article{Marsaglia:1986:IFC,
author = "George Marsaglia",
title = "The incomplete {$ \Gamma $} function as a continuous
{Poisson} distribution",
journal = j-COMPUT-MATH-APPL-B,
volume = "12",
number = "5--6",
pages = "1187--1190",
month = sep # "\slash " # dec,
year = "1986",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(86)90242-7",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
ZMnumber = "0628.65149",
abstract = "The paper illustrates the use of the incomplete $
\Gamma $ function as a means for computer generation of
Poisson random variables.",
abstract-2 = "Among the many contributions of Professor Luke to the
theory of special functions, the most useful in
computational statistics is probably that on the
incomplete $\Gamma$ function. This short paper points
out that an incomplete $\Gamma$ function routine is so
important that it should be a standard part of any
library of statistical subroutines. The paper goes on
to give another example of use of the incomplete
$\Gamma$ function: as a means for computer generation
of Poisson random variables. and, having urged wide use
of the incomplete $\Gamma$ function, proceeds with
development of a Poisson generator whose principal aim
is to avoid use of the very function it has previously
lauded. Occasional use of an accurate incomplete
$\Gamma$ routine is essential however, in order that
the composite method be exact.",
fjournal = "Computers and Mathematics with Applications. Part B",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
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",
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 = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
ZMnumber = "0614.65002",
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) $. Moreover, the
proposed algorithm can be implemented on a computer
without using more data storage than the existing
algorithms.",
fjournal = "Ars Combinatoria. The Canadian Journal of
Combinatorics",
journal-URL = "http://www.combinatorialmath.ca/arscombinatoria/",
keywords = "algorithms; average time complexity; random number
generation; squaring histogram method; worst-case
complexity",
ZMclass = "*65C10 Random number generation",
}
@Article{Marsaglia:1989:CAA,
author = "George Marsaglia and Arif Zaman and Youlu Zheng",
title = "{C309}: An Algorithm for the Area of the Union of a
Collection of Convex Sets",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "31",
number = "1",
pages = "46--49",
month = "????",
year = "1989",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949658908811112",
ISSN = "0094-9655 (print), 1563-5163 (electronic)",
ISSN-L = "0094-9655",
bibdate = "Thu Aug 05 09:22:20 2004",
bibsource = "http://jscs.stat.vt.edu/JSCS/articles/v31n1.html;
http://jscs.statjournals.net/;
http://web.lums.edu.pk/~arifz/resume.html;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.tandf.co.uk/journals/titles/00949655.html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
}
@InCollection{Marsaglia:1989:CGD,
author = "George Marsaglia",
title = "The {$ 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 = "http://www.math.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",
DOI = "https://doi.org/10.2307/2008355",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65L05 (65Q05)",
MRnumber = "90h:65124",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database; MathSciNet database",
ZMnumber = "0675.65073",
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)]' = 2
f(x - 1), $ $ X V'(x) = - V(x - 1) $ and $ [X W(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",
journal-URL = "http://www.ams.org/mcom/",
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",
ZMreviewer = "P. I. Ialamov",
}
@InProceedings{Marsaglia:1989:RVS,
author = "George Marsaglia",
title = "Random Variables for Supercomputers",
crossref = "Wegman:1988:SIC",
pages = "103--103",
year = "1989",
bibdate = "Wed Nov 12 16:33:35 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "Abstract only.",
URL = "http://www.dtic.mil/dtic/tr/fulltext/u2/a205068.pdf",
abstract = "A discussion of methods for generating random
variables in supercomputers, particularly the 205 and
ETA 10. Methods that exploit vector processing are
well-suited for generating uniform random variables,
both integer and real, and several of them are
described. For non-uniform variates, however, methods
that have proved best for conventional computers do not
readily yield to vector methods. For example, the best
methods for normal or exponential variates in
conventional computers take less than $ 1.2 T $, where
$T$ is the time for a uniform variate, yet in
supercomputers those methods take relatively much
longer. Different approaches to reducing these times
will be discussed.",
acknowledgement = ack-nhfb,
}
@Article{Marsaglia:1990:DBR,
author = "George Marsaglia and B. Narasimhan and Arif Zaman",
title = "The distance between random points in rectangles",
journal = j-COMMUN-STAT-THEORY-METH,
volume = "19",
number = "11",
pages = "4199--4212",
year = "1990",
CODEN = "CSTMDC",
DOI = "https://doi.org/10.1080/03610929008830437",
ISSN = "0361-0926 (print), 1532-415X (electronic)",
ISSN-L = "0361-0926",
MRclass = "60D05 (62E15)",
MRnumber = "92b:60015",
bibdate = "Wed Jan 27 05:38:53 MST 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/communstattheorymeth1990.bib;
http://www.math.utah.edu/pub/tex/bib/fortran3.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
MathSciNet database",
ZMnumber = "0731.60012",
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.",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics: Theory and Methods",
journal-URL = "http://www.tandfonline.com/loi/lsta20",
keywords = "Fortran program; random distance between the points",
ZMclass = "60D05 Geometric probability 60-04 Machine computation,
programs (probability theory)",
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",
DOI = "https://doi.org/10.2307/2324749",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "41A60 (01A50 05A10)",
MRnumber = "92b:41049",
MRreviewer = "E. Rodney Canfield",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib;
MathSciNet database",
ZMnumber = "0786.05007",
abstract = "A derivation of Stirling's formula $ n! \sim n^n
e^{-n} \sqrt {2 \pi n^n} $ is presented. To this
purpose the authors consider the relation $ n! =
\int^\infty_0 x^n e^{-x} \, d x $. 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",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
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",
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",
month = oct,
year = "1990",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(90)90033-W",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
MRclass = "65C10",
MRnumber = "1 076 268",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
MathSciNet database",
ZMnumber = "0997.65510",
abstract = "It is now possible to do serious scientific work on
personal computers (PC's). Many simulation studies,
whether exploratory or for production runs, call for
random numbers. We offer here a new kind of random
number generator with implementation tailored
specifically for PC's using Intel 8088/8086 or
80286/80386 processors. A floating-point coprocessor is
not required or even useful for the generator,
although, of course, a coprocessor may help other parts
of a simulation. The generator has an extremely long
period --- some 2^{1407} --- requires only 43 stored
values and uses only one arithmetic operation:
subtraction. It is one of a new class of generators
that we have recently developed. They are called
add-with-carry and subtract-with-borrow generators.
Related to lagged-Fibonacci generators, the new class
has an interesting underlying theory, astonishingly
long periods and provable uniformity for full
sequences. This article describes a machine language
subroutine that provides 32-bit random integers as well
as uniform (single precision) reals with standard
24-bit fractions.",
fjournal = "Computer Physics Communications. An International
Journal and Program Library for Computational Physics
and Physical Chemistry",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
ZMclass = "*65C10 Random number generation",
}
@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",
month = jan,
year = "1990",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/0167-7152(90)90092-L",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "65C10",
MRnumber = "91a:65008",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/1990.bib;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
ZMnumber = "0692.65001",
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",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "arithmetic sequence; Fortran implementation;
independence test; lagged-Fibonacci generator;
randomness test; universal random number generator",
ZMclass = "*65C10 Random number generation",
ZMreviewer = "K. Uosaki",
}
@Article{Zaman:1990:RSS,
author = "Arif Zaman and George Marsaglia",
title = "Random Selection of Subsets with Specified Element
Probabilities",
journal = j-COMMUN-STAT-THEORY-METH,
volume = "19",
number = "11",
pages = "4419--4434",
month = "????",
year = "1990",
CODEN = "CSTMDC",
DOI = "https://doi.org/10.1080/03610929008830448",
ISSN = "0361-0926 (print), 1532-415x (electronic)",
ISSN-L = "0361-0926",
bibdate = "Thu Aug 05 06:44:44 2004",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
abstract = "A lottery ticket consists of a choice of 6 numbers,
all different, from 1 to 49. Most probability analysis
assumes that this is like sampling without replacement
from an urn. On the other hand, it is well known that
many people pick 'lucky' numbers such as 7 and 11 more
frequently than 'ordinary' numbers such as 17 or 26.
For some lotteries, information is available on the
frequencies with which players have chosen each of the
numbers from 1 to 49. This raises the interesting
question of finding distributions on the $ 49 \choose 6
$ possible ticket choices that will be consistent with
the frequencies specified for each of the elements. We
develop several methods for doing this; some of them
may be extended to the next stages of the problem, when
enough information is available from the Lottery to
specify frequencies of pairs or even triples, and one
seeks distributions on the 6-tuples consistent with
those frequencies.",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics. Theory and Methods",
journal-URL = "http://www.tandfonline.com/loi/lsta20",
}
@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 = aug,
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1214/aoap/1177005878",
ISSN = "1050-5164",
MRclass = "65C10",
MRnumber = "92h:65009",
MRreviewer = "Renata Rotondi",
bibdate = "Mon Aug 02 11:01:47 2004",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
MathSciNet database",
URL = "http://projecteuclid.org/euclid.aoap/1177005878",
ZMnumber = "0733.65005",
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.",
abstract-2 = "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 $2^{1751}$ bits, or a sequence of
$2^{1376}$ 32-bit integers, or a sequence of $2^{931}$
reals with 24-bit fractions--all using simple computer
arithmetic (subtraction) and a few memory locations.",
acknowledgement = ack-nhfb,
fjournal = "The Annals of Applied Probability",
journal-URL = "http://projecteuclid.org/all/euclid.aoap/;
http://www.jstor.org/journals/10505164.html",
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",
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 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Mon Jun 2 19:03:29 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jsuper.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",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
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 = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
series = "Proc. Sympos. Appl. Math.",
ZMnumber = "0776.65005",
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",
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 = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
note = "See report of cryptographic insecurity of KISS
generator \cite{Rose:2011:KBT}. See also
\cite{Robert:1999:MCS}.",
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:LHR,
author = "George Marsaglia and Arif Zaman",
title = "Letter: How Random Is Random Enough?",
journal = j-SCIENCE-NEWS,
volume = "143",
number = "11",
pages = "163--163",
day = "13",
month = mar,
year = "1993",
CODEN = "SCNEBK",
ISSN = "0036-8423 (print), 1943-0930 (electronic)",
ISSN-L = "0036-8423",
bibdate = "Wed Jun 22 06:40:26 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "Cautionary comment on \cite{Peterson:1992:MCP}.",
URL = "http://www.jstor.org/stable/10.2307/3977245",
acknowledgement = ack-nhfb,
ajournal = "Sci. News (Washington, DC)",
fjournal = "Science News (Washington, DC)",
journal-URL = "http://www.jstor.org/journals/00368423.html;
http://www.sciencenews.org/view/archives;
http://www3.interscience.wiley.com/journal/122396840/home",
}
@Article{Marsaglia:1993:MTR,
author = "George Marsaglia and Arif Zaman",
title = "Monkey Tests for Random Number Generators",
journal = j-COMPUT-MATH-APPL,
volume = "26",
number = "9",
pages = "1--10",
month = nov,
year = "1993",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(93)90001-C",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65C10",
MRnumber = "1 236 767",
bibdate = "Mon Aug 02 10:36:54 2004",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/tomacs.bib;
MathSciNet database",
note = "See also \cite{Percus:1995:TAM}.",
ZMnumber = "0788.65007",
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",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
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.",
ZMreviewer = "K. Uosaki (Tottori)",
}
@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 = "http://www.math.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-COMPUT-MATH-APPL,
volume = "26",
number = "8",
pages = "31--42",
month = oct,
year = "1993",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(93)90329-T",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "68P10",
MRnumber = "94h:68041",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
ZMnumber = "0800.68353",
fjournal = "Computers \& Mathematics with Applications. An
International Journal",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "efficient algorithm; interpolation search; searching
ordered tables",
ZMclass = "*68P10 Searching and sorting 65C99 Numerical
simulation",
}
@Article{Marsaglia:1993:TCR,
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",
DOI = "https://doi.org/10.1145/159544.376068",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Jan 28 14:57:13 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1990.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
remark = "Marsaglia criticizes the `minimal-standard generator'
proposed in \cite{Park:1988:RNG} and discusses fast
ways to compute LCGs with particular multipliers. See
new test in \cite{Sullivan:1993:ATR} and responses in
\cite{Park:1993:ATR}.",
}
@Misc{Marsaglia:1994:MAR,
author = "George Marsaglia",
title = "The mother of all random generators",
howpublished = "Web document",
month = oct,
year = "1994",
bibdate = "Tue Jun 21 18:41:45 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "ftp://ftp.taygeta.com/pub/c/mother.c",
acknowledgement = ack-nhfb,
}
@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",
day = "15",
month = mar,
year = "1994",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/0167-7152(94)90174-0",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "65U05",
MRnumber = "1 278 658",
bibdate = "Thu Dec 22 07:42:24 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fortran3.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/statproblett1990.bib;
MathSciNet database",
URL = "http://www.sciencedirect.com/science/article/pii/0167715294901740",
ZMnumber = "0798.65132",
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 $$
c P h i(x) = (2 / \pi)^{1 / 2} \int^\infty_x \exp ( -
t^2 / 2) d t = u, $$ 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 & l t; 32 $, $ 0 \le j & l t; 32 $ and $ 0 \le m
& l t; 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.",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
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)",
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 = "https://doi.org/10.1063/1.168514",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Mon Aug 02 17:54:20 2004",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers in Physics",
journal-URL = "http://scitation.aip.org/content/aip/journal/cip",
remark = "ran2() range is [1,2147483562], with period about
2.3e+18. mzran13() has range[0,2147483647] and period
about 2^125 = 4.25e37.",
}
@Misc{Marsaglia:1994:YAR,
author = "George Marsaglia",
title = "Yet another rug",
howpublished = "Posted to the electronic billboard {\tt
sci.stat.math}.",
day = "1",
month = aug,
year = "1994",
bibdate = "Thu Jan 05 15:49:10 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
}
@Misc{Marsaglia:1995:MRN,
author = "George Marsaglia",
title = "The {Marsaglia} Random Number {CDROM} including the
{Diehard Battery of Tests} of Randomness",
howpublished = "Web site at the Department of Statistics, Florida
State University, Tallahassee, FL, USA.",
year = "1995",
bibdate = "Sat Mar 03 07:40:23 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://stat.fsu.edu/pub/diehard/",
acknowledgement = ack-nhfb,
}
@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",
month = jul,
year = "1995",
CODEN = "????",
DOI = "https://doi.org/10.1111/j.1467-9574.1995.tb01460.x",
ISSN = "0039-0402 (print), 1467-9574 (electronic)",
ISSN-L = "0039-0402",
MRclass = "62E10",
MRnumber = "96d:62013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
ZMnumber = "0831.62015",
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",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9574",
keywords = "canonical form; characterizations; exponential
distribution; independent digits; independent integer
and fractional parts; positive differentiable
densities",
onlinedate = "29 April 2008",
ZMclass = "*62E10 Structure theory of statistical distributions
60E05 General theory of probability distributions",
}
@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 = "http://www.math.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,
}
@Misc{Marsaglia:1997:RNG,
author = "George Marsaglia",
title = "A random number generator for {C}",
howpublished = "Posted to the {\tt sci.math.num-analysis} news group",
day = "29",
month = sep,
year = "1997",
bibdate = "Thu Dec 20 20:21:51 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
note = "From the posting: ``Keep the following six lines of
code somewhere in your files.
\#define znew ((z=36969*(z\&65535)+(z>>16))<<16)
\#define wnew ((w=18000*(w\&65535)+(w>>16))\&65535)
\#define IUNI (znew+wnew) \#define UNI
(znew+wnew)*4.656613e-10 static unsigned long
z=362436069, w=521288629; void setseed(unsigned long
i1,unsigned long i2){z=i1; w=i2;}
Whenever you need random integers or random reals in
your C program, just insert those six lines at (near?)
the beginning of the program. In every expression where
you want a random real in [0,1) use UNI, or use IUNI
for a random 32-bit integer. No need to mess with
ranf() or ranf(lastI), etc, with their requisite
overheads. Choices for replacing the two multipliers
36969 and 18000 are given below. Thus you can tailor
your own in-line multiply-with-carry random number
generator.''",
URL = "http://mathforum.org/kb/thread.jspa?messageID=1607565",
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 = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jstatsoft.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,
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
}
@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",
DOI = "https://doi.org/10.1145/292395.292453",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65C10 (60E99)",
MRnumber = "99k:65014",
bibdate = "Mon Feb 8 17:51:43 MST 1999",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib;
MathSciNet database",
URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p341-marsaglia/",
ZMnumber = "0930.65002",
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",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
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",
}
@Misc{Marsaglia:1999:RNC,
author = "George Marsaglia",
title = "Random numbers for {C}: The {END}?",
howpublished = "Message-ID {\tt 36A5FC62.17C9CC33@stat.fsu.edu}.
Posting to the {\tt sci.crypt.random-numbers}, {\tt
sci.math}, and {\tt sci.stat.math} news groups.",
day = "20",
month = jan,
year = "1999",
bibdate = "Thu Dec 20 20:22:58 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://groups.google.com/group/sci.crypt/browse_thread/thread/ca8682a4658a124d/",
acknowledgement = ack-nhfb,
}
@TechReport{Marsaglia:19xx:TNP,
author = "George Marsaglia",
title = "Tables of the Normal Probability Measure of an Offset
Circle",
type = "Report",
number = "??",
institution = inst-BOEING-SRL,
address = inst-BOEING-SRL:adr,
month = "????",
year = "19xx",
bibdate = "Wed Nov 12 07:44:53 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
}
@Unpublished{Marsaglia:2000:ADS,
author = "J. C. Marsaglia and G. Marsaglia",
title = "The {Anderson--Darling--Savage} goddess-of-fit test",
year = "2000",
bibdate = "Tue Apr 17 07:50:11 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "Unpublished. See
\cite{Anderson:1952:ATC,Savage:1957:ITR}.",
acknowledgement = ack-nhfb,
remark = "Was this ever published? It is cited at
http://www.cs.hku.hk/cisc/projects/va/ and
www.csis.hku.hk/cisc/download/idetect/, but is not
found in the Elsevier or Springer databases on 17 April
2012, nor by three major Web engines.",
}
@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 = "http://www.math.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 = "https://doi.org/10.1145/358407.358414",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65C10 (65C60)",
MRnumber = "2001k:65015",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib;
MathSciNet database",
fjournal = "Association for Computing Machinery. Transactions on
Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
http://www.math.utah.edu/pub/tex/bib/matlab.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}.",
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
}
@Unpublished{Marsaglia:2001:MOF,
author = "George Marsaglia",
title = "Memoranda to {Office of Florida State Courts
Administrator}",
year = "2001",
bibdate = "Wed Jun 22 07:31:13 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
note = "February 5, 2001 and May 29, 2001, with
recommendations on jury selection.",
acknowledgement = ack-nhfb,
}
@Article{Marsaglia:2001:PUC,
author = "George Marsaglia",
title = "Problems with the Use of Computers for Selecting Jury
Panels",
journal = "Jurimetrics",
volume = "41",
number = "??",
pages = "425--427",
month = "Summer",
year = "2001",
CODEN = "JURIFF",
ISSN = "0897-1277",
bibdate = "Tue Jun 21 19:10:26 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://heinonline.org/HOL/Page?handle=hein.journals/juraba41&div=38&g_sent=1&collection=journals",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.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 = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/cryptography2000.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,
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
}
@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 = "http://www.math.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,
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
}
@InCollection{Marsaglia:2003:MCM,
author = "George Marsaglia",
title = "{Monte Carlo} method",
crossref = "Ralston:2003:ECS",
pages = "1192--1193",
year = "2003",
bibdate = "Wed Jun 22 06:58:50 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
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 = "http://www.math.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,
fjournal = "Journal of Modern Applied Statistical Methods",
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",
DOI = "https://doi.org/10.1145/769800.769827",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Sep 3 17:06:36 MDT 2003",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/cacm2000.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@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",
DOI = "https://doi.org/10.18637/jss.v008.i14",
ISSN = "1548-7660",
ISSN-L = "1548-7660",
bibdate = "Tue Dec 16 17:06:19 2003",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/tomacs.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 also
\cite{Salmon:2011:PRN,Saito:2012:DCS,Steele:2014:FSP}
for the failure of Marsaglia's {\tt xorwow()} generator
from this paper. See
\cite{Panneton:2005:XRN,Vigna:2016:EEM} 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,
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
}
@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",
year = "2004",
CODEN = "JSSOBK",
DOI = "https://doi.org/10.18637/jss.v011.i05",
ISSN = "1548-7660",
ISSN-L = "1548-7660",
bibdate = "Sat Dec 04 09:18:40 2004",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/tomacs.bib",
note = "See
\cite{Marsaglia:2003:XR,Panneton:2005:XRN,Vigna:2016:EEM}.
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,
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
submitted = "2004-07-07",
}
@Article{Marsaglia:2004:BURa,
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 = "https://doi.org/10.1016/j.spl.2003.11.001",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "65C10",
MRnumber = "2 029 733",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
MathSciNet database",
URL = "http://www.doornik.com/research/randomdouble.pdf",
ZMnumber = "02041513",
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",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "64-bit floating point; Random number generators;
Seeds",
ZMclass = "*62-99 Statistics",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jstatsoft.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,
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
}
@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 = "http://www.math.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,
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
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 = "http://www.math.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,
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
submitted = "2004-06-05",
xxpages = "1--11",
}
@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",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.jstatsoft.org/counter.php?id=138&url=v14/i13&ct=2;
http://www.jstatsoft.org/counter.php?id=138&url=v14/i13/v14i13.pdf&ct=1",
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,
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
keywords = "$\chi^2$; goodness of fit; monkey tests; overlapping
m-tuples",
submitted = "2005-05-01",
}
@Article{Marsaglia:2005:RPO,
author = "George Marsaglia",
title = "On the Randomness of Pi and Other Decimal Expansions",
journal = "{InterStat}: statistics on the {Internet}",
pages = "17",
month = oct,
year = "2005",
CODEN = "????",
ISSN = "1941-689X",
bibdate = "Wed Jun 22 10:34:43 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://interstat.statjournals.net/INDEX/Oct05.html;
http://interstat.statjournals.net/YEAR/2005/articles/0510005.pdf",
abstract = "Tests of randomness much more rigorous than the usual
frequency-of-digit counts are applied to the decimal
expansions of $ \pi $, $e$ and $ \sqrt {2} $, using the
Diehard Battery of Tests adapted to base 10 rather than
the original base 2. The first $ 10^9 $ digits of $ \pi
$, $e$ and $ \sqrt {2} $ seem to pass the Diehard tests
very well. But so do the decimal expansions of most
rationals $ k / p $ with large primes $p$. Over the
entire set of tests, only the digits of $ \sqrt {2} $
give a questionable result: the monkey test on 5-letter
words. Its significance is discussed in the
text.\par
Three specific $ k / p $ are used for comparison. The
cycles in their decimal expansions are developed in
reverse order by the multiply-with-carry (MWC) method.
They do well in the Diehard tests, as do many fast and
simple MWC RNGs that produce base-$b$ `digits' of the
expansions of $ k / p $ for $ b = 2^{32} $ or $ b =
2^{32} - 1 $. Choices of primes $p$ for such MWC RNGs
are discussed, along with comments on their
implementation.",
abstract-2 = "Extensive tests of randomness used to distinguish good
from not-so-good random number generators are applied
to the digits of $\pi$, $e$ and $\sqrt{2}$, as well as
to rationals $k / p$ for large primes $p$. They seem to
pass these tests as well as some of the best RNGs, and
could well serve in their stead if the digits could be
easily and quickly produced in the computer---and they
can, at least for rationals $k / p$. Simple and fast
methods are developed to produce, in reverse order, for
large primes $p$ and general bases $b$, the periodic
cycles of the base-$b$ expansions of $k / p$. Specific
choices provide high quality, fast and simple RNGs with
periods thousands of orders of magnitude greater than
what are currently viewed as the longest. Also included
are historical references to decimal expansions and
their relation to current, often wrong, website
discussions on the randomness of $\pi$.",
acknowledgement = ack-nhfb,
keywords = "Diehard Tests; Pi; Random Number Generators; Tests of
Randomness",
}
@Article{Marsaglia:2006:RCS,
author = "George Marsaglia",
title = "Refutation of claims such as {``Pi is less random than
we thought''}",
journal = "{InterStat}: statistics on the {Internet}",
day = "23",
month = jan,
year = "2006",
CODEN = "????",
ISSN = "1941-689X",
bibdate = "Tue Jun 21 19:08:05 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://interstat.statjournals.net/YEAR/2006/articles/0601001.pdf",
abstract = "In article by Tu and Fischman in a Physics journal
\cite{Tu:2005:SRD} has led to worldwide reports that Pi
is less random than we thought, or that Pi is not the
best random number generator, or that Pi seems good but
not the best. A careful examination of the Tu and
Fischman procedure shows that it is needlessly
complicated and can be reduced to study of the average
value of $ (U_2 - U_1) (U_2 - U_3) $ for uniform
variates U produced by a RNG, (but not on their
distribution). The authors' method of assigning a
letter grade, A+, A, B, C, D, E to a sample mean, based
on its distance from the expected value, suggests
naivety in the extreme. Application, in the present
article, to the first 960 million digits of the
expansion of Pi shows that they perform as well as
other RNGs on not only the average for $ (U_2 - U_1)
(U_2 - U_3) $, but on the more difficult test for their
distribution, consistent with results previously shown
in this journal that Pi does quite well on far more
extensive and difficult-to-pass tests of randomness.",
acknowledgement = ack-nhfb,
keywords = "Diehard Tests; LSTests of Randomness; Pi; Random
Number Generators",
}
@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",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
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
/ (1.01 b - 0.2713) $ and variance $ \sigma^2 = (a^2 +
1) / (b^2 + 0.108 b - 3.795) \mu^2 $.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
pubdates = "Submitted 2006-03-07; Accepted 2006-05-11",
}
@Misc{Marsaglia:2010:SKR,
author = "George Marsaglia",
title = "{SUPER KISS} random-number generator",
howpublished = "Web posting",
day = "3",
month = nov,
year = "2010",
bibdate = "Mon Dec 31 17:17:20 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.velocityreviews.com/forums/t704080-re-rngs-a-super-kiss.html",
acknowledgement = ack-nhfb,
remark = "This note introduces source code for an extension of
the KISS generator Marsaglia:1993:KG that combines it
with others to produce a generator with a period of $
54767 \times 2^{1337279} \approx 10^{402 \, 565} $.",
}
@Misc{Marsaglia:2011:RPE,
author = "George Marsaglia",
title = "{RNGs} with periods exceeding $ 10^{\hbox {40
million}} $",
howpublished = "Message-ID {\tt
<603ebe15-a32f-4fbb-ba44-6c73f7919a33@t35g2000yqj.googlegroups.com>}
in newsgroups {\tt sci.math}, {\tt comp.lang.c} and
{\tt sci.crypt}.",
day = "16",
month = jan,
year = "2011",
bibdate = "Wed Jun 22 18:06:30 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
}
%%% ====================================================================
%%% Papers cross-referenced by Marsaglia bibliography entries, or
%%% citing Marsaglia in their titles:
@Article{Anderson:1952:ATC,
author = "T. W. Anderson and D. A. Darling",
title = "Asymptotic theory of certain `goodness of fit'
criteria based on stochastic processes",
journal = j-ANN-MATH-STAT,
volume = "23",
number = "2",
pages = "193--212",
month = jun,
year = "1952",
CODEN = "AASTAD",
ISSN = "0003-4851",
bibdate = "Tue Apr 17 07:38:55 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.jstor.org/stable/2236446",
abstract = "The statistical problem treated is that of testing the
hypothesis that $n$ independent, identically
distributed random variables have a specified
continuous distribution function $ F(x) $.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
}
@Article{Savage:1957:ITR,
author = "Richard Savage",
title = "On the Independence of Tests of Randomness and Other
Hypotheses",
journal = j-J-AM-STAT-ASSOC,
volume = "52",
number = "277",
pages = "53--57",
month = mar,
year = "1957",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:32 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314156;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1950.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.jstor.org/stable/2281400",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@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 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib;
http://www.math.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",
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{VanGelder:1967:SNR,
author = "A. {Van Gelder}",
title = "Some New Results in Pseudo-Random Number Generation",
journal = j-J-ACM,
volume = "14",
number = "4",
pages = "785--792",
month = oct,
year = "1967",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321420.321437",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Tue Nov 1 09:50:45 1994",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jacm.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
abstract = "Pseudo-random number generators of the power residue
(sometimes called congruential or multiplicative) type
are discussed and results of statistical tests
performed on specific examples of this type are
presented. Tests were patterned after the methods of
MacLaren and Marsaglia (M\&M). The main result
presented is the discovery of several power residue
generators which performed well in these tests. This is
important because, of all the generators using standard
methods (including power residue) that were tested by
M\&M, none gave satisfactory results. The overall
results here provide further evidence for their
conclusion that the types of tests usually encountered
in the literature do not provide an adequate index of
the behavior of n-tuples of consecutively generated
numbers. In any Monte Carlo or simulation problem where
n supposedly independent random numbers are required at
each step, this behavior is likely to be important.
Finally, since the tests presented here differ in
certain details from those of M\&M, some of their
generators were retested as a check. A cross-check
shows that results are compatible; in particular, if a
generator failed one of their tests badly, it also
failed the present author's corresponding test badly.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Westlake:1967:URN,
author = "W. J. Westlake",
title = "A Uniform Random Number Generator Based on the
Combination of Two Congruential Generators",
journal = j-J-ACM,
volume = "14",
number = "2",
pages = "337--340",
month = apr,
year = "1967",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321386.321396",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Dec 22 07:42:23 2011",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jacm.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
abstract = "A method of generating pseudo-random uniform numbers
based on the combination of two congruential generators
is described. It retains two of the desirable features
of congruential generators, namely, the long cycle and
the case of implementation on a digital computer.
Furthermore, unlike the method of combining
congruential generators recently proposed by MacLaren
and Marsaglia, it does not require the retention in
computer memory of a table of generated numbers. The
generator gave completely satisfactory results on a
fairly stringent series of statistical tests.",
acknowledgement = ack-nhfb,
descriptors = "RNG",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@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 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:26 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
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",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "PRNG (pseudo-random number generator)",
references = "7",
}
@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",
CODEN = "VMMAA3",
ISSN = "0024-0850",
MRclass = "65C10",
MRnumber = "85a:65015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
ZMnumber = "0551.60020",
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, Seriya 1:
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",
}
@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 (print), 1558-1586 (electronic)",
ISSN-L = "0161-1194",
bibdate = "Sat Nov 21 12:35:16 MST 1998",
bibsource = "http://www.dean.usma.edu/math/pubs/cryptologia/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/cryptologia.bib",
note = "See also letters and responses, Cryptologia {\bf 8},
1984, pp. 374--378.",
acknowledgement = ack-nhfb,
fjournal = "Cryptologia",
journal-URL = "http://www.tandfonline.com/loi/ucry20",
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 (print), 1558-1586 (electronic)",
ISSN-L = "0161-1194",
bibdate = "Sat Nov 21 12:35:16 MST 1998",
bibsource = "http://www.dean.usma.edu/math/pubs/cryptologia/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/cryptologia.bib",
acknowledgement = ack-nhfb,
fjournal = "Cryptologia",
journal-URL = "http://www.tandfonline.com/loi/ucry20",
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 (print), 1432-1785 (electronic)",
ISSN-L = "0025-2611",
MRclass = "65C10 (11K45)",
MRnumber = "90c:65011",
MRreviewer = "J. Patrick Lambert",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
ZMnumber = "0663.65006",
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",
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 = "MTRKA8",
ISSN = "0026-1335 (print), 1435-926X (electronic)",
ISSN-L = "0026-1335",
MRclass = "65C10",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
ZMnumber = "0653.65006",
abstract = "A recursive congruential non-additive generator of the
form $ (1) \quad x_{n + 1} \equiv f(x_n)(m o d 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 (m o d 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 = 1z}_i w^d_i (m o
d 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",
fjournal = "Metrika. International Journal for Theoretical and
Applied Statistics",
journal-URL = "http://link.springer.com/journal/184",
keywords = "Marsaglia's lattice test; nonlinear generators; pseudo
random number generators; recursive congruential
non-additive generator",
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 = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:28 MDT 2003",
bibsource = "ftp://ftp.uu.net/library/bibliography;
http://portal.acm.org/;
http://www.adahome.com/Resources/Bibliography/articles.ref;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGADA Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
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{Ferrenberg:1992:MCS,
author = "A. M. Ferrenberg and D. P. Landau and Y. J. Wong",
title = "{Monte Carlo} simulations: Hidden errors from `good'
random number generators",
journal = j-PHYS-REV-LET,
volume = "69",
number = "23",
pages = "3382--3384",
day = "7",
month = dec,
year = "1992",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.69.3382",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Sun Dec 18 09:16:59 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "See also \cite{Grassberger:1993:CGR}.",
URL = "http://prl.aps.org/abstract/PRL/v69/i23/p3382_1",
abstract = "The Wolff algorithm is now accepted as the best
cluster-flipping Monte Carlo algorithm for beating
``critical slowing down.'' We show how this method can
yield incorrect answers due to subtle correlations in
``high quality'' random number generators.",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
remark = "This paper is cited for its revelations about the
sensitivity of Monte Carlo simulations to the
underlying random-number generator. From the paper:\par
Page 3383: ``Surprisingly, we find that the use of the
`high quality' generators together with the Wolff
algorithm produces systematically incorrect results.
\ldots{} Runs made using the SWC generator gave better
results, but even these data showed noticeable
systematic errors which had the opposite sign from
those produced using R250. In contrast, data obtained
using the simple 32-bit congruential generator CONG
produced answers which were correct to within the error
bars. Even use of the mixed generator SWCW did not
yield results which were free of bais, although the
systematic errors were much smaller.''\par From page
3384: ``extensive Monte Carlo simulations on an Ising
model for which the exact answers are known have shown
that ostensibly high quality random number generators
may lead to subtle, but dramatic, systematic errors for
some algorithms, but not others. Since there is no
reason to believe that the model which we have
investigated has any special idiosyncrasies, these
results offer another stern warning about the need to
very carefully test the implementation of new
algorithms. In particular, this means that a specific
algorithm must be tested together with the random
number generator being used {\em regardless} of the
tests which the generator has passed.''",
remark-corr = "See \cite{Kalle:1984:PRN, Berdnicov:1991:MCS,
Ferrenberg:1992:MCS, Grassberger:1993:CGR,
Kankaala:1993:BLC, Selke:1993:CFM, Coddington:1994:ARN,
Holian:1994:PNG, Vattulainen:1994:PTR,
Compagner:1995:OCR, Schmid:1995:EMC,
Vattulainen:1995:CSS, Vattulainen:1995:PMT,
Bromley:1996:QNG, Coddington:1997:RNG, Shchur:1997:CMC,
Shchur:1997:SDR, DSouza:1998:SBD, Gammel:1998:HRR,
Resende:1998:URN, Mertens:2003:EPR, Bauke:2004:PRC,
Mertens:2004:EPR, Ossola:2004:SED} for examples of
generator correlations causing Monte Carlo simulations
in physics to converge to the wrong answer.",
}
@Article{Peterson:1992:MCP,
author = "I. Peterson",
title = "{Monte Carlo} Physics: {A} Cautionary Lesson",
journal = j-SCIENCE-NEWS,
volume = "142",
number = "25--26",
pages = "422--422",
day = "19",
month = dec,
year = "1992",
CODEN = "SCNEBK",
ISSN = "0036-8423 (print), 1943-0930 (electronic)",
ISSN-L = "0036-8423",
bibdate = "Sat Mar 03 07:52:46 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "Comment on negative experience with the
Marsaglia--Zaman generator reported in
\cite{Ferrenberg:1992:MCS}. See response
\cite{Marsaglia:1993:LHR}.",
URL = "http://www.jstor.org/stable/4018020",
acknowledgement = ack-nhfb,
ajournal = "Sci. News (Washington, DC)",
fjournal = "Science News (Washington, DC)",
journal-URL = "http://www.jstor.org/journals/00368423.html;
http://www.sciencenews.org/view/archives;
http://www3.interscience.wiley.com/journal/122396840/home",
}
@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",
DOI = "https://doi.org/10.1145/210330.210331",
ISSN = "1049-3301 (print), 1558-1195 (electronic)",
ISSN-L = "1049-3301",
bibdate = "Thu Aug 7 12:05:30 MDT 2003",
bibsource = "http://dblp.uni-trier.de/db/journals/tomacs/tomacs5.html#PercusW95;
http://www.acm.org/pubs/contents/journals/tomacs/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/tomacs.bib",
note = "See \cite{Marsaglia:1993:MTR}.",
ZMnumber = "0853.65009",
abstract-1 = "A theoretical analysis is given for a new test, the
``Monkey'' test, for pseudorandom number sequences,
which was proposed by Marsaglia. Selected results,
using the test on several pseudorandom number
generators in the literature, are also presented.",
abstract-2 = "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.",
fjournal = "ACM Transactions on Modeling and Computer Simulation",
journal-URL = "http://portal.acm.org/browse_dl.cfm?&idx=J781",
keywords = "empirical tests; Marsaglia's monkey test; pseudorandom
number generators",
oldlabel = "PercusW95",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/tomacs/PercusW95",
ZMreviewer = "B. Mathiszik (Halle)",
}
@Article{Dyadkin:1997:FEL,
author = "Iosif G. Dyadkin and Kenneth G. Hamilton",
title = "A family of enhanced {Lehmer} random number
generators, with hyperplane suppression, and direct
support for certain physical applications",
journal = j-COMP-PHYS-COMM,
volume = "107",
number = "1--3",
pages = "258--280",
day = "22",
month = dec,
year = "1997",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(97)00101-X",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
MRclass = "65C10 86-08 86A20",
bibdate = "Thu Nov 14 10:49:00 2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib",
URL = "http://www.cpc.cs.qub.ac.uk/cpc/;
http://www.cpc.cs.qub.ac.uk/cpc/cgi-bin/list_summary.pl?CatNumber=ADGW",
ZMnumber = "0938.65006",
abstract = "Over two hundred congruential pseudorandom number
generators, each with a different multiplier, are built
into a single assembler routine that returns 32-bit
integer and floating-point values. This gives a Monte
Carlo user the opportunity of selecting a combination
of sequences, so as to provide a greater appearance of
chaos. The software makes use of extended 64-bit
arithmetic on Intel 386/387 (or higher) chips, thus
attaining a period of 262 for each of the individual
generators. The routine also features entry points that
more directly support certain applications, such as
well logging in nuclear geophysics. In addition to the
customary uniform (0,1) ``white noise'' generator, the
package provides values distributed according to the
exponential and Gaussian distributions, random unit
vectors in two and three dimensions, as well as
Klein--Nishina and neutron scattering distributions.",
acknowledgement = ack-nhfb,
annote = "This paper describes a Fortran-callable Intel IA-32
assembly language implementation of a family of 200
pseudo-random number generators, based on earlier work
\cite{Dyadkin:1997:SBM}, with associated routines for
generating several distributions (uniform, exponential,
Gaussian, 2-D and 3-D unit vectors, plus several
specific to physics applications). It contains a good
discussion of randomness-testing procedures, and
comparisons with other algorithms, including the
ziggurat method
\cite{Marsaglia:1984:FEI,Marsaglia:2000:ZMG} used in
Matlab version 5 and later \cite{Moler:2001:CCN}. The
software is available from the CPC Library, for a fee,
and with use restrictions.",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
keywords = "RNLEHMER200 (Intel IA-32 assembly language, 4044
Lines)",
}
@Article{Dyadkin:1997:SBM,
author = "Iosif G. Dyadkin and Kenneth G. Hamilton",
title = "A study of $ 64 $-bit multipliers for {Lehmer}
pseudorandom number generators",
journal = j-COMP-PHYS-COMM,
volume = "103",
number = "2--3",
pages = "103--130",
month = jul,
year = "1997",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(97)00052-0",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
MRclass = "65C10",
MRnumber = "98f:65013",
bibdate = "Thu Nov 14 11:03:33 2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib",
ZMnumber = "0980.65007",
abstract = "A study was conducted of multipliers for 64-bit
congruential pseudorandom number generators. Extensive
analysis and testing resulted in the identification of
over $ 200 $ good multipliers of the form $ A = 5^k $,
where $k$ is a prime number. The integer lattice
structure from any single multiplier is so fine that it
is not visible when {\tt REAL*4} values are returned in
up to four dimensions. Known number-theoretic
characteristics of $ m = 2^l $ generators were
exploited to provide a remarkably sensitive new lattice
test, one that is based on analysis of spacings in
several dimensions. That examination led to new methods
that can provide lattice-free pseudorandom streams in
up to 200 dimensions, and with extended period
length.",
acknowledgement = ack-nhfb,
annote = "This is the theoretical work behind the software
\cite{Dyadkin:1997:FEL}. The linear-congruential
generators have multipliers of the form $ A = 5^k \bmod
2^{64} $, where $k$ is a prime number, and testing has
identified more than 200 suitable values of $k$. This
work was later updated for 128-bit arithmetic
\cite{Dyadkin:2000:SBM}.",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Bach:1998:EPM,
author = "Eric Bach",
title = "Efficient prediction of {Marsaglia--Zaman} random
number generators",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "44",
number = "3",
pages = "1253--1257",
year = "1998",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/18.669305",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
MRclass = "65C10",
MRnumber = "99b:65007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
ZMnumber = "0915.65003",
abstract = "This paper presents two properties of the random
number generator by {\it G. Marsaglia} and {\it A.
Zaman} [Ann. Appl. Probab. 1, No. 3, 462-480 (1991; Zbl
0733.65005)]. First, it is shown that its successive
digits are digits of certain rational $b$-adic numbers.
Then, an efficient algorithm is derived to predict an
unknown pseudorandom sequence of this type. Two
examples of the prediction are given.",
classmath = "*65C10 Random number generation 11K45 Pseudo-random
numbers, etc.",
fjournal = "Institute of Electrical and Electronics Engineers.
Transactions on Information Theory",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
keywords = "$b$-adic number; algorithm; continued fraction;
pseudo-random number generator",
ZMreviewer = "K. Uosaki (Tottori)",
}
@Book{Robert:1999:MCS,
author = "Christian P. Robert and George Casella",
title = "{Monte Carlo} statistical methods",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxi + 507",
year = "1999",
ISBN = "0-387-98707-X",
ISBN-13 = "978-0-387-98707-1",
LCCN = "QA276 .R575 1999",
bibdate = "Wed Jun 22 08:52:43 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
z3950.loc.gov:7090/Voyager",
series = "Springer texts in statistics",
acknowledgement = ack-nhfb,
remark = "Section 2.1.2 gives a description of the
Marsaglia\slash Zaman KISS generator.",
subject = "Mathematical statistics; Monte Carlo method",
}
@Article{Dyadkin:2000:SBM,
author = "Iosif G. Dyadkin and Kenneth G. Hamilton",
title = "A study of 128-bit multipliers for congruential
pseudorandom number generators",
journal = j-COMP-PHYS-COMM,
volume = "125",
number = "1--3",
pages = "239--258",
month = mar,
year = "2000",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(99)00467-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Nov 14 11:21:52 2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib",
URL = "http://cpc.cs.qub.ac.uk/summaries/ADLK;
http://www.elsevier.com/gej-ng//10/15/40/55/25/42/abstract.html",
abstract = "A study was conducted of multipliers for 128-bit
congruential pseudorandom number generators. Extensive
analysis and testing resulted in the identification of
over 2000 good multipliers of the form $ A = 5^k \bmod
2^{128} $, where $k$ is a prime number. The integer
lattice structure from any single multiplier is so fine
that it is not visible when {\tt REAL*8} values are
returned in up to four dimensions, or {\tt REAL*4}
values in seven dimensions. The multipliers are
designed to be used in sets, and are suitable for use
in massively-parallel computation.",
acknowledgement = ack-nhfb,
annote = "This paper extends the authors' earlier work on 64-bit
generators \cite{Dyadkin:1997:FEL,Dyadkin:1997:SBM} to
128-bit arithmetic and more than 2000 generators, each
with a different multiplier.",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
keywords = "Congruential; General purpose; Monte Carlo;
Multipliers; Pseudorandom; Random number generators;
Random numbers; Statistical methods",
}
@TechReport{Moler:2001:CCN,
author = "Cleve B. Moler",
title = "{Cleve}'s Corner: Normal Behavior: {Ziggurat}
algorithm generates normally distributed random
numbers",
type = "Technical note",
institution = inst-MATHWORKS,
address = inst-MATHWORKS:adr,
pages = "1",
month = "Spring",
year = "2001",
bibdate = "Thu Oct 24 07:16:21 2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/matlab.bib",
URL = "http://www.mathworks.com/company/newsletter/clevescorner/spring01_cleve.shtml",
acknowledgement = ack-nhfb,
annote = "See \cite{Marsaglia:2000:ZMG} for the algorithm used
in Matlab's (version 5 and later) randn() function for
generating normally-distributed pseudo-random
numbers.",
keywords = "Matlab",
}
@Book{Robert:2004:MCS,
author = "Christian P. Robert and George Casella",
title = "{Monte Carlo} statistical methods",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xxx + 645",
year = "2004",
ISBN = "0-387-21239-6",
ISBN-13 = "978-0-387-21239-5",
LCCN = "QA276 .R575 2004",
bibdate = "Wed Jun 22 08:52:43 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
z3950.loc.gov:7090/Voyager",
series = "Springer texts in statistics",
URL = "http://www.loc.gov/catdir/enhancements/fy0818/2004049157-d.html;
http://www.loc.gov/catdir/enhancements/fy0818/2004049157-t.html;
http://www.springer.com/statistics/statistical+theory+and+methods/book/978-0-387-21239-5",
acknowledgement = ack-nhfb,
subject = "Mathematical statistics; Monte Carlo method; MCMCM
(Markov Chain Monte Carlo Methods)",
tableofcontents = "Introduction \\
Random Variable Generation \\
Monte Carlo Integration \\
Controlling Monte Carlo Variance \\
Monte Carlo Optimization \\
Markov Chains \\
The Metropolis--Hastings Algorithm \\
The Slice Sampler \\
The Two-Stage Gibbs Sampler \\
The Multi-Stage Gibbs Sampler \\
Variable Dimension Models and Reversible Jump \\
Diagnosing Convergence \\
Perfect Sampling \\
Iterated and Sequential Importance Sampling",
}
@Article{Leong:2005:CIZ,
author = "Philip H. W. Leong and Ganglie Zhang and Dong-U",
title = "A Comment on the Implementation of the Ziggurat
Method",
journal = j-J-STAT-SOFT,
volume = "12",
number = "7",
pages = "1--44",
month = "????",
year = "2005",
CODEN = "JSSOBK",
ISSN = "1548-7660",
bibdate = "Wed May 18 11:18:51 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
note = "See \cite{Marsaglia:2000:ZMG}.",
URL = "http://www.jstatsoft.org/counter.php?id=114&url=v12/i07&ct=2;
http://www.jstatsoft.org/counter.php?id=114&url=v12/i07/v12i07.pdf&ct=1",
abstract = "We show that the short period of the uniform random
number generator in the published implementation of
Marsaglia and Tsang's Ziggurat method for generating
random deviates can lead to poor distributions.
Changing the uniform random number generator used in
its implementation fixes this issue.",
accepted = "2005-02-08",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
submitted = "2005-02-08",
}
@Article{Panneton:2005:XRN,
author = "Fran{\c{c}}ois Panneton and Pierre L'Ecuyer",
title = "On the xorshift random number generators",
journal = j-TOMACS,
volume = "15",
number = "4",
pages = "346--361",
month = oct,
year = "2005",
CODEN = "ATMCEZ",
DOI = "https://doi.org/10.1145/1113316.1113319",
ISSN = "1049-3301 (print), 1558-1195 (electronic)",
ISSN-L = "1049-3301",
bibdate = "Thu Feb 16 10:42:56 MST 2006",
bibsource = "http://www.acm.org/pubs/contents/journals/tomacs/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/tomacs.bib",
note = "See
\cite{Marsaglia:2003:XR,Brent:2004:NMX,Vigna:2016:EEM}.",
abstract = "G. Marsaglia recently introduced a class of very fast
xorshift random number generators, whose implementation
uses three ``xorshift'' operations. They belong to a
large family of generators based on linear recurrences
modulo 2, which also includes shift-register
generators, the Mersenne twister, and several others.
In this article, we analyze the theoretical properties
of xorshift generators, search for the best ones with
respect to the equidistribution criterion, and test
them empirically. We find that the vast majority of
xorshift generators with only three xorshift
operations, including those having good
equidistribution, fail several simple statistical
tests. We also discuss generators with more than three
xorshifts.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Modeling and Computer Simulation",
journal-URL = "http://portal.acm.org/browse_dl.cfm?&idx=J781",
}
@Article{Tu:2005:SRD,
author = "Shu-Ju Tu and Ephraim Fischbach",
title = "A Study on the Randomness of the Digits of $ \pi $",
journal = j-INT-J-MOD-PHYS-C,
volume = "16",
number = "2",
pages = "281--294",
month = feb,
year = "2005",
CODEN = "IJMPEO",
DOI = "https://doi.org/10.1142/S0129183105007091",
ISSN = "0129-1831 (print), 1793-6586 (electronic)",
bibdate = "Wed Jun 22 11:19:42 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
note = "The statistical analysis in this work is flawed; see
\cite{Marsaglia:2005:RPO,Marsaglia:2006:RCS}",
URL = "http://www.worldscinet.com/ijmpc/16/1602/S01291831051602.html",
abstract = "We apply a newly-developed computational method,
Geometric Random Inner Products (GRIP), to quantify the
randomness of number sequences obtained from the
decimal digits of $ \pi $. Several members from the
GRIP family of tests are used, and the results from $
\pi $ are compared to those calculated from other
random number generators. These include a recent
hardware generator based on an actual physical process,
turbulent electroconvection. We find that the decimal
digits of $ \pi $ are in fact good candidates for
random number generators and can be used for practical
scientific and engineering computations.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Modern Physics C [Physics and
Computers]",
journal-URL = "http://www.worldscientific.com/loi/ijmpc",
}
@Article{Agapie:2010:RPH,
author = "Stefan C. Agapie and Paula A. Whitlock",
title = "Random packing of hyperspheres and {Marsaglia}'s
parking lot test",
journal = j-MONTE-CARLO-METHODS-APPL,
volume = "16",
number = "3--4",
pages = "197--209",
month = dec,
year = "2010",
CODEN = "MCMAC6",
DOI = "https://doi.org/10.1515/mcma.2010.019",
ISSN = "0929-9629 (print), 1569-3961 (electronic)",
ISSN-L = "0929-9629",
MRclass = "65C05 (65C10)",
MRnumber = "2747812",
bibdate = "Wed Feb 29 09:27:54 MST 2012",
bibsource = "http://www.degruyter.com/view/j/mcma.2010.16.issue-3/issue-files/mcma.2010.16.issue-3.xml;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/mcma.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.degruyter.com/view/j/mcma.2010.16.issue-3-4/mcma.2010.019/mcma.2010.019.xml",
acknowledgement = ack-nhfb,
fjournal = "Monte Carlo Methods and Applications",
journal-URL = "http://www.degruyter.com/view/j/mcma",
keywords = "CDC 48-bit multiplicative congruential generator {\tt
rannyu()}",
remark = "The authors investigate the connection between the
hypersphere packing problem and Marsaglia's parking lot
test \cite{Marsaglia:1985:CVR} for correlations in
random number generator output.",
}
@Article{Anonymous:2011:OGM,
author = "Anonymous",
title = "Obituary: {George Marsaglia (1924--2011)}",
journal = "{Tallahassee Democrat}",
pages = "??--??",
day = "22",
month = feb,
year = "2011",
ISSN = "0738-5153",
bibdate = "Mon Jan 07 18:23:00 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://www.legacy.com/obituaries/tallahassee/obituary.aspx?n=george-marsaglia",
acknowledgement = ack-nhfb,
}
@TechReport{Rose:2011:KBT,
author = "Greg Rose",
title = "{KISS}: {A} Bit Too Simple",
type = "Report",
number = "??",
institution = "Qualcomm Inc.",
address = "????",
day = "18",
month = apr,
year = "2011",
bibdate = "Wed Jun 22 08:40:22 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
URL = "http://eprint.iacr.org/2011/007.pdf",
abstract = "KISS (`Keep it Simple Stupid') is an efficient
pseudo-random number generator originally specified by
G. Marsaglia and A. Zaman in 1993. G. Marsaglia in 1998
posted a C version to various USENET newsgroups,
including sci.crypt. Marsaglia himself has never
claimed cryptographic security for the KISS generator,
but others have made the intellectual leap and claimed
that it is of cryptographic quality. In this paper we
show a number of reasons why the generator does not
meet some of the KISS authors' claims, why it is not
suitable for use as a stream cipher, and that it is not
cryptographically secure. Our best attack requires
about 70 words of generated output and a few hours of
computation to recover the initial state. In early
2011, G. Marsaglia posted a new version of KISS, which
falls to a simple divide-and-conquer attack.",
acknowledgement = ack-nhfb,
}
@InProceedings{Salmon:2011:PRN,
author = "John K. Salmon and Mark A. Moraes and Ron O. Dror and
David E. Shaw",
title = "Parallel random numbers: as easy as $ 1, 2, 3 $",
crossref = "Lathrop:2011:SPI",
pages = "16:1--16:12",
year = "2011",
DOI = "https://doi.org/10.1145/2063384.2063405",
bibdate = "Fri Dec 16 11:05:47 MST 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
http://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/supercomputing2011.bib;
http://www.math.utah.edu/pub/tex/bib/tomacs.bib",
abstract = "Most pseudorandom number generators (PRNGs) scale
poorly to massively parallel high-performance
computation because they are designed as sequentially
dependent state transformations. We demonstrate that
independent, keyed transformations of counters produce
a large alternative class of PRNGs with excellent
statistical properties (long period, no discernable
structure or correlation). These counter-based PRNGs
are ideally suited to modern multicore CPUs, GPUs,
clusters, and special-purpose hardware because they
vectorize and parallelize well, and require little or
no memory for state. We introduce several counter-based
PRNGs: some based on cryptographic standards (AES,
Threefish) and some completely new (Philox). All our
PRNGs pass rigorous statistical tests (including
TestU01's BigCrush) and produce at least 264 unique
parallel streams of random numbers, each with period
2128 or more. In addition to essentially unlimited
parallel scalability, our PRNGs offer excellent
single-chip performance: Philox is faster than the
CURAND library on a single NVIDIA GPU.",
acknowledgement = ack-nhfb,
articleno = "16",
remark-1 = "From the article, page 3: ``The period of any useful
PRNG must be sufficiently long that the state space of
the PRNG will not be exhausted by any application, even
if run on large parallel machines for long periods of
time. One million cores, generating 10 billion random
numbers per second, will take about half an hour to
generate $2^{64}$ random numbers, which raises doubts
about the long-term viability of a single,
unpararameterized PRNG with a periods of `only'
$2^{64}$. On the other hand, exhausting the state space
of a multistreamable family of $2^{32}$ such
generators, or a single generator with a period of
$2^{128}$, is far beyond the capability of any
technology remotely like that in current computers.''",
remark-2 = "From the article, page 5: ``only a few conventional
PRNGs pass even one complete battery of Crush tests.
The multiple recursive generators, the multiplicative
lagged Fibonacci generators, and some combination
generators are reported to do so. On the other hand,
many of the most widely used PRNGs fail quite
dramatically, including all of the linear congruential
generators, such as drand48() and the C-language
rand(). The linear and general feedback shift register
generators, including the Mersenne Twister, always fail
the tests of linear dependence, and some fail many
more.''",
remark-3 = "This article has a good discussion of the issues of
parallel random-number generation. The authors note
that large internal state (e.g., the Mersenne Twister
needs 2496 bytes) is impractical with a million cores,
or with GPUs that require awkward memory transfers
between GPU and CPU memory. They propose methods that
require little state, and are based on cryptographic
algorithms. They point out that a generator based on
the Advanced Encryption Standard with Intel AES-NI
hardware support becomes competitive with other
generators. The comparative Table 2 on page 8 shows
that the Threefish, Threefry, and Philox generators
require only 0.7 to 4.3 cycles per byte.",
}
@Misc{Saito:2012:DCS,
author = "Mutsuo Saito and Makoto Matsumoto",
title = "A deviation of {CURAND}: Standard pseudorandom number
generator in {CUDA} for {GPGPU}",
howpublished = "Slides presented at the Tenth International Conference
on Monte Carlo and Quasi-Monte Carlo Methods in
Scientific Computing",
month = feb,
year = "2012",
bibdate = "Wed May 13 11:21:03 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/tomacs.bib",
URL = "http://www.mcqmc2012.unsw.edu.au/slides/MCQMC2012_Matsumoto.pdf",
acknowledgement = ack-nhfb,
remark = "The slides report that Marsaglia's {\tt xorwow()}
long-period ($ (2^{160} - 1) 2^{32}$) generator
\cite{Marsaglia:2003:XR} is rejected by three of the
BigCrush tests (Collision Over, Simplified Poker Test,
and Linear Complexity Test) in the TESTU01 suite, and
the authors conclude: ``{\tt xorwow} is not suitable
for serious Monte Carlo''.",
}
@Article{Steele:2014:FSP,
author = "Guy L. {Steele, Jr.} and Doug Lea and Christine H.
Flood",
title = "Fast splittable pseudorandom number generators",
journal = j-SIGPLAN,
volume = "49",
number = "10",
pages = "453--472",
month = oct,
year = "2014",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/2714064.2660195",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue May 12 17:41:21 MDT 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/java2010.bib;
http://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
http://www.math.utah.edu/pub/tex/bib/multithreading.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/sigplan2010.bib;
http://www.math.utah.edu/pub/tex/bib/tomacs.bib",
abstract = "We describe a new algorithm SplitMix for an
object-oriented and splittable pseudorandom number
generator (PRNG) that is quite fast: 9 64-bit
arithmetic/logical operations per 64 bits generated. A
conventional linear PRNG object provides a generate
method that returns one pseudorandom value and updates
the state of the PRNG, but a splittable PRNG object
also has a second operation, split, that replaces the
original PRNG object with two (seemingly) independent
PRNG objects, by creating and returning a new such
object and updating the state of the original object.
Splittable PRNG objects make it easy to organize the
use of pseudorandom numbers in multithreaded programs
structured using fork-join parallelism. No locking or
synchronization is required (other than the usual
memory fence immediately after object creation).
Because the generate method has no loops or
conditionals, it is suitable for SIMD or GPU
implementation. We derive SplitMix from the DotMix
algorithm of Leiserson, Schardl, and Sukha by making a
series of program transformations and engineering
improvements. The end result is an object-oriented
version of the purely functional API used in the
Haskell library for over a decade, but SplitMix is
faster and produces pseudorandom sequences of higher
quality; it is also far superior in quality and speed
to java.util.Random, and has been included in Java JDK8
as the class java.util.SplittableRandom. We have tested
the pseudorandom sequences produced by SplitMix using
two standard statistical test suites (DieHarder and
TestU01) and they appear to be adequate for
``everyday'' use, such as in Monte Carlo algorithms and
randomized data structures where speed is important.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
remark-1 = "OOPSLA '14 conference proceedings.",
remark-2 = "On page 466, the authors describe an interesting
technique for improving a user-supplied seed that might
produce insufficient randomness in the next several
members of the random-number sequence: ``Long runs of
0-bits or of 1-bits in the $\gamma$ [candidate seed]
value do not cause bits of the seed to flip; an
approximate proxy for how many bits of the seed will
flip might be the number of bit pairs of the form 01 or
10 in the candidate $\gamma$ value {\tt z}. Therefore
we require that the number of such pairs, as computed
by {\tt Long.bitCount(z ^ (z >>> 1))}, exceed 24; if it
does not, then the candidate z is replaced by the XOR
of {\tt z} and {\tt 0xaaaaaaaaaaaaaaaaL}, a constant
chosen so that (a) the low bit of {\tt z} remains 1,
and (b) every bit pair of the form 00 or 11 becomes
either 01 or 10, and likewise every bit pair of the
form 01 or 10 becomes either 00 or 11, so the new value
necessarily has more than 24 bit pairs whose bits
differ. Testing shows that this trick appears to be
effective.''",
remark-3 = "From page 468: ``we did three runs of TestU01 BigCrush
on {\tt java.util.Random}; 19 tests produced clear
failure on all three runs. These included 9 Birthday
Spacings tests, 8 ClosePairs tests, a WeightDistrib
test, and a CouponCollector test. This confirms
L'Ecuyer's observation that {\tt java.util.Random}
tends to fail Birthday Spacings tests [17].'' The
reference is to \cite{LEcuyer:2001:SUR}.",
remark-4 = "From page 470: ``[L'Ecuyer] comments, `In the Java
class {\tt java.util.Random}, RNG streams can be
declared and constructed dynamically, without limit on
their number. However, no precaution seems to have been
taken regarding the independence of these streams.'''",
remark-5 = "From page 471: ``They [the generators in this paper]
should not be used for cryptographic or security
applications, because they are too predictable (the
mixing functions are easily inverted, and two
successive outputs suffice to reconstruct the internal
state), \ldots{} One version seems especially suitable
for use as a replacement for {\tt java.util.Random},
because it produces sequences of higher quality, is
faster in sequential use, is easily parallelized for
use in JDK8 stream expressions, and is amenable to
efficient implementation on SIMD and GPU
architectures.''",
}
@Article{Vigna:2016:EEM,
author = "Sebastiano Vigna",
title = "An Experimental Exploration of {Marsaglia}'s {\tt
xorshift} Generators, Scrambled",
journal = j-TOMS,
volume = "42",
number = "4",
pages = "30:1--30:23",
month = jul,
year = "2016",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2845077",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Nov 22 17:45:24 MST 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/tomacs.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://dl.acm.org/citation.cfm?id=2845077",
abstract = "Marsaglia proposed xorshift generators are a class of
very fast, good-quality pseudorandom number generators.
Subsequent analysis by Panneton and L'Ecuyer has
lowered the expectations raised by Marsaglia's article,
showing several weaknesses of such generators.
Nonetheless, many of the weaknesses of xorshift
generators fade away if their result is scrambled by a
nonlinear operation (as originally suggested by
Marsaglia). In this article we explore the space of
possible generators obtained by multiplying the result
of a xorshift generator by a suitable constant. We
sample generators at 100 points of their state space
and obtain detailed statistics that lead us to choices
of parameters that improve on the current ones. We then
explore for the first time the space of
high-dimensional xorshift generators, following another
suggestion in Marsaglia's article, finding choices of
parameters providing periods of length $ 2^{1024} 1 $
and $ 2^{4096} 1 $. The resulting generators are of
extremely high quality, faster than current similar
alternatives, and generate long-period sequences
passing strong statistical tests using only eight
logical operations, one addition, and one
multiplication by a constant.",
acknowledgement = ack-nhfb,
articleno = "30",
}
%%% ====================================================================
%%% These entries must come last because they are cross-referenced
%%% by others above.
@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 = "http://www.math.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 = "http://www.math.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",
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LCCN = "QA221 .A66",
bibdate = "Thu Aug 05 06:10:49 2004",
bibsource = "http://www.math.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",
ISBN-13 = "978-0-12-775950-0",
LCCN = "QA297 .A67",
bibdate = "Mon Aug 02 10:53:03 2004",
bibsource = "http://www.math.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 = "????",
ISBN-13 = "????",
ISSN = "0318-6288",
LCCN = "QA276.A1 S92 1974",
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series = "Carleton mathematical lecture notes",
acknowledgement = ack-nhfb,
}
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editor = "Anthony Ralston and Chester L. Meek",
booktitle = "Encyclopedia of computer science",
title = "Encyclopedia of computer science",
publisher = "Petrocelli\slash Charter",
address = "New York, NY, USA",
pages = "xxviii + 1523",
year = "1976",
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LCCN = "QA76.15 .E55 1976",
bibdate = "Mon Aug 02 16:32:11 2004",
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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",
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LCCN = "QA76.15 .E48 1983",
bibdate = "Mon Aug 02 10:58:31 2004",
bibsource = "http://www.math.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",
ISBN-13 = "978-0-444-87725-3",
LCCN = "QA276.4 .S95 1984",
bibdate = "Thu Dec 18 13:41:50 2003",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Wegman:1988:CSS,
editor = "Edward J. Wegman and Donald T. Gantz and John J.
Miller",
title = "{Computing Science and Statistics Proceedings of the
20th Symposium on the Interface Fairfax, Virginia,
April 1988}",
publisher = "American Statistical Association",
address = "Alexandria, VA, USA",
pages = "xxxvii + 860",
year = "1988",
bibdate = "Wed Nov 12 16:41:33 2014",
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URL = "http://www.dtic.mil/dtic/tr/fulltext/u2/a208838.pdf",
acknowledgement = ack-nhfb,
}
@Proceedings{Wegman:1988:SIC,
editor = "Edward J. Wegman",
booktitle = "{20th Symposium on the Interface: Computing Science
and Statistics: Theme: Computationally Intensive
Methods in Statistics April 20--23, 1988}",
title = "{20th Symposium on the Interface: Computing Science
and Statistics: Theme: Computationally Intensive
Methods in Statistics April 20--23, 1988}",
publisher = "Interface Foundation of North America, Inc.",
address = "P.O. Box 7460, Fairfax Station, VA 22039-7460, USA",
pages = "iv + 185",
year = "1988",
bibdate = "Wed Nov 12 16:36:54 2014",
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URL = "http://www.dtic.mil/dtic/tr/fulltext/u2/a205068.pdf",
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",
ISBN-13 = "978-0-387-97076-9, 978-3-540-97076-7",
LCCN = "QA273.18 .C683 1989",
bibdate = "Thu Aug 05 06:19:18 2004",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Burr:1992:UEN,
editor = "Stefan A. Burr",
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",
ISBN-13 = "978-0-8218-5501-0",
LCCN = "QA241 .U67 1992",
bibdate = "Thu Aug 05 06:26:07 2004",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
series = "Proceedings of symposia in applied mathematics",
acknowledgement = ack-nhfb,
tableofcontents = "The unreasonable effectiveness of number theory in
physics, communication and music / Manfred R. Schroeder
[1--20] \\
The reasonable and unreasonable effectiveness of number
theory in statistical mechanics / George E. Andrews
[21--34]\\
Number theory and dynamical systems / J.C. Lagarias
[35--72] \\
The mathematics of random number generators / George
Marsaglia [73--90] \\
Cyclotomy and cyclic codes / Vera Pless [91--104] \\
Number theory in computer graphics / M. Douglas McIlroy
[105--122]",
}
@Article{Grassberger:1993:CGR,
author = "Peter Grassberger",
title = "On correlations in ``good'' random number generators",
journal = j-PHYS-LET-A,
volume = "181",
number = "1",
pages = "43--46",
day = "27",
month = sep,
year = "1993",
CODEN = "PYLAAG",
DOI = "https://doi.org/10.1016/0375-9601(93)91122-L",
ISSN = "0375-9601 (print), 1873-2429 (electronic)",
ISSN-L = "0375-9601",
bibdate = "Wed Feb 22 09:13:21 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "See \cite{Ferrenberg:1992:MCS}.",
URL = "http://www.sciencedirect.com/science/article/pii/037596019391122L",
abstract = "By studying a different system, we verify the
correlations found recently in a popular random number
generator by Ferrenberg et al. We find indeed that the
dominant correlations are too long ranged to be seen by
them, and we check a number of further RNGs.",
acknowledgement = ack-nhfb,
fjournal = "Physics Letters A",
journal-URL = "http://www.sciencedirect.com/science/journal/03759601",
remark-corr = "See \cite{Kalle:1984:PRN, Berdnicov:1991:MCS,
Ferrenberg:1992:MCS, Grassberger:1993:CGR,
Kankaala:1993:BLC, Selke:1993:CFM, Coddington:1994:ARN,
Holian:1994:PNG, Vattulainen:1994:PTR,
Compagner:1995:OCR, Schmid:1995:EMC,
Vattulainen:1995:CSS, Vattulainen:1995:PMT,
Bromley:1996:QNG, Coddington:1997:RNG, Shchur:1997:CMC,
Shchur:1997:SDR, DSouza:1998:SBD, Gammel:1998:HRR,
Resende:1998:URN, Mertens:2003:EPR, Bauke:2004:PRC,
Mertens:2004:EPR, Ossola:2004:SED} for examples of
generator correlations causing Monte Carlo simulations
in physics to converge to the wrong answer.",
}
@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",
ISBN-13 = "978-0-442-27679-9",
LCCN = "QA76.15 .E48 1993",
bibdate = "Mon Aug 02 10:58:31 2004",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/adabooks.bib",
acknowledgement = ack-nhfb,
}
@Book{Ralston:2003:ECS,
editor = "Anthony Ralston and Edwin D. Reilly and David
Hemmendinger",
booktitle = "Encyclopedia of Computer Science",
title = "Encyclopedia of Computer Science",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Fourth",
bookpages = "xxix + 2034",
pages = "xxix + 2034",
year = "2003",
ISBN = "0-470-86412-5",
ISBN-13 = "978-0-470-86412-8",
LCCN = "QA76.15 .E48 2003",
bibdate = "Wed Jun 22 06:58:50 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.e-streams.com/es0707/es0707\_3357.htm;
http://www.loc.gov/catdir/bios/wiley046/2003283283.htm;
http://www.loc.gov/catdir/description/wiley041/2003283283.htm;
http://www.loc.gov/catdir/toc/wiley041/2003283283.htm",
acknowledgement = ack-nhfb,
remark = "Previously published: London : Nature Publishing
Group, 2000.",
subject = "Computer science; Encyclopedias; Information science",
}
@Proceedings{Lathrop:2011:SPI,
editor = "Scott Lathrop and Jim Costa and William Kramer",
booktitle = "{SC'11: Proceedings of 2011 International Conference
for High Performance Computing, Networking, Storage and
Analysis, Seattle, WA, November 12--18 2011}",
title = "{SC'11: Proceedings of 2011 International Conference
for High Performance Computing, Networking, Storage and
Analysis, Seattle, WA, November 12--18 2011}",
publisher = pub-ACM # " and " # pub-IEEE,
address = pub-ACM:adr # " and " # pub-IEEE:adr,
bookpages = "866",
pages = "866",
year = "2011",
DOI = "https://doi.org/10.1145/2063384",
ISBN = "1-4503-0771-X",
ISBN-13 = "978-1-4503-0771-0",
LCCN = "QA76.5 .S96 2011",
bibdate = "Fri Dec 16 11:11:35 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
http://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
http://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/supercomputing2011.bib",
acknowledgement = ack-nhfb,
xxeditor = "{ACM}",
}