 | Java Number Cruncher: The Java Programmer's Guide to Numerical Computing
By Ronald Mak
| | Table of Contents | | | | Chapter 14. Generating Random Numbers |
References Beckmann, Peter, A History of Pi , New York: St. Martin's Press, 1971.
Beckmann discusses the Monte Carlo technique and Buffon's needle algorithm in Chapter 15. Both topics are also covered by McCracken. Knuth, Donald E., The Art of Computer Programming, Volume 2: Seminumerical Algorithms , 3rd edition, Reading, MA: Addison-Wesley, 1998.
The classic reference for random number generation is Chapter 3 of this book. It contains proofs for the polar and ratio algorithms for generating normally distributed random values, as well as for the logarithm algorithm for generating exponentially distributed random values. McCracken, Daniel D., "The Monte Carlo Method," 1955. In Computers and Computations , edited by R. R. Fenichel and J. Weizenbaum, San Francisco: W. H. Freeman and Company, 1971. Monahan, John F., Numerical Methods of Statistics , Cambridge, UK: Cambridge University Press, 2001.
Section 11.3 of this book proves the ratio algorithm, along with the von Neumann algorithm for generating exponentially distributed random values.  |
