Page 121 - Computational Statistics Handbook with MATLAB

108 Computational Statistics Handbook with MATLAB

There has been considerable research into methods for random number
generation, and we refer the reader to the sources mentioned below for more
information on the theoretical foundations. The book by Ross [1997] is an
excellent resource and is suitable for advanced undergraduate students. He
addresses simulation in general and includes a discussion of discrete event
simulation and Markov chain Monte Carlo methods. Another text that covers
the topic of random number generation and Monte Carlo simulation is Gen-
tle [1998]. This book includes an extensive discussion of uniform random
number generation and covers more advanced topics such as Gibbs sam-
pling. Two other resources on random number generation are Rubinstein
[1981] and Kalos and Whitlock [1986]. For a description of methods for gen-
erating random variables from more general multivariate distributions, see
Johnson [1987]. The article by Deng and Lin [2000] offers improvements on
some of the standard uniform random number generators.
A recent article in the MATLAB News & Notes [Spring, 2001] describes the
method employed in MATLAB for obtaining normally distributed random
variables. The algorithm that MATLAB uses for generating uniform random
numbers is described in a similar newsletter article and is available for down-
load at:

www.mathworks.com/company/newsletter/pdf/Cleve.pdf.

© 2002 by Chapman & Hall/CRC