This section lists some of the source reference material used in programming the random generators and distributions. The following is a list of source articles or books from which the generator and distribution objects were implemented
LCG. a golden oldie; see [Knuth, 1981] or [Numerical Recipes].
PMMLCG. see [Miller, 1988].
ACG. a golden oldie; see [Knuth, 1981] or [Numerical Recipes].
SCG. a golden oldie; see [Knuth, 1981] or [Numerical Recipes].
SWB. see [Marsaglia, 1991]
PSWB. see [Marsaglia, 1991]
MRG. see [L'Ecuyer, A]
C2MRG3. see [L'Ecuyer, B]
C2TAUS. see [Tezuka & L'Ecuyer, 1991]
TT403/TT775/TT800 (TGFSR). see [Tezuka & L'Ecuyer, 1991]
MT19937. By Matsumoto and Nishimura. Code posted in 1997 to the pLab web site
MWCA, MWCB, C3MWC, RWC2, RWC8 ("Mother"). Report posted to sci.stat.consult and sci.math.num-analysis by Bob Wheeler on behalf of George Marsaglia on October 28, 1994. Code found at: ftp://ftp.taygeta.com/pub/c/mother.c
C2LCGX. See [L'Ecuyer & Cote, 1991]
C4LCGX. See [L'Ecuyer & Andres, 1996]
RandomBitDist. Code contributed by Nelson Minar <nelson@media.mit.edu>.
BernoulliDist. Code contributed by Barry McMullin <mcmullin@santafe.edu>.
UniformIntegerDist. Code contributed by Nelson Minar <nelson@media.mit.edu>.
UniformUnsignedDist. Code contributed by Nelson Minar <nelson@media.mit.edu>.
UniformDoubleDist. Code contributed by Nelson Minar <nelson@media.mit.edu>.
NormalDist. [Numerical Recipes].
LogNormalDist. [Numerical Recipes].
ExponentialDist. Russell, 1992 (citation forthcoming).
GammaDist. [Watkins, 1994].
Pierre L'Ecuyer maintains a personal web site . He has many of his own papers there, as well as further links. He has papers both on generating random numbers and on testing random number generators.
George Marsaglia has a personal web site. His battery of tests for random generators, called Diehard, is not available there, but rather from Hong Kong. A GUI version of Diehard has been under development for some time, but is not yet ready.
The pLab project in Salzburg, Austria, also has much useful information.
[Ferrenberg, 1992] Alan M. Ferrenberg, D. P. Landau, and Y. Joanna Wong, "Monte Carlo Simulations: Hidden Errors from "Good" Random Number Generators": Physical Review Letters, no. 23, vol. 69, December, 1992.
[Knuth, 1981] Donald Knuth, The Art of Computer Programming, 2nd ed., vol. II, Seminumerical Algorithms, Addison-Wesley, Reading, 1981.
[L'Ecuyer, A] Pierre L'Ecuyer, "A Search for Good Multiple Recursive Random Generators." Unpublished: see personal website.
[L'Ecuyer, B] Pierre L'Ecuyer, "Combined Multiple Recursive Random Number Generators." Unpublished: see personal website.
[L'Ecuyer & Andres, 1996] Pierre L'Ecuyer and Terry H. Andres, "A Random Number Generator Based on the Combination of Four LCGs.": Mathematics and Computers in Simulation To appear: see personal website, no. 1, vol. 17, 17 December 1996.
[L'Ecuyer & Cote, 1991] Pierre L'Ecuyer and Serge Cote, "Implementing a Random Number Package with Splitting Facilities": ACM TOMACS, no. 1, vol. 17, pp. 98-111, March, 1991.
[Marsaglia, 1991] George Marsaglia and Arif Zaman, "A New Class of Random Number Generators.": Annals of Applied Probability, no. 3, vol. 3, pp. 462-480.
[Matsumoto & Kurita, 1996] Makoto Matsumoto and Yoshiharu Kurita, "Twisted GFSR Generators II.": ACM TOMACS (Amended by K. Matsumoto, 8 July 1996)., no. 3, vol. 4, pp. 254-266.
[Miller, 1988] Stephen K. Park and Keith W. Miller, "Random Number Generators: Good Ones Are Hard to Find.": CACM, no. 10, vol. 31, pp. 1192-1201, October 1988.
[Numerical Recipes] W. H. Press, S. A Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed., Cambridge University Press, 1992.