Simulating Random Numbers from Specific Distributions

Abstract

For the important distributions, specialized algorithms based on the general methods discussed in the previous chapter are available. The important difference in the algorithms is their speed. A secondary difference is the size and complexity of the program to implement the algorithm. Because all of the algorithms for generating from nonuniform distributions rely on programs to generate from uniform distributions, an algorithm that uses only a small number of uniforms to yield a variate of the target distribution may be faster on a computer system on which the generation of the uniform is very fast. As we have mentioned, on a given computer system there may be more than one program available to generate uniform deviates. Often a portable generator is slower than a nonportable one, so for portable generators of nonuniform distributions those that require a small number of uniform deviates may be better. If evaluation of elementary functions is a part of the algorithm for generating random deviates, then the speed of the overall algorithm depends on the speed of the evaluation of the functions. The relative speed of elementary function evaluation is different on different computer systems.