Non-Uniform Random Number Generation: A Survey And Tutorial

Abstract

The basic pseudo-random number generators on computers return deviates which are uniformly distributed in the interval between 0 and 1. For simulations and other applications other random variables are needed which follow given statistical distributions, for instance normal deviates. The survey will concentrate on the most important distributions arising in simulation applications. The considered non-uniform distributions fall into two categories: continuous and discrete. In either class very efficient methods for sampling from general distributions are presented. Specific cases considered include the exponential, normal, gamma, beta and Cauchy distributions in the continuous, and Poisson, binomial and hypergeometric generators in the discrete category. In selecting suitable specific algorithms for each distribution we rejected the 'easiest' methods which are not fast enough. On the other hand, some of the most efficient generators are rather difficult to implement. The selected algorithms are almost as fast as these, but not too complex. Their Fortran versions are portable except for the employed basic (0, 1)-uniform generators for which, however, the user may substitute his or her own favorite. A number of the proposed methods are the author's recent developments. Some well-known alternatives will also be mentioned.