The Exact-Approximation Method for Generating Random Variables in a Computer

A suitably chosen approximation to the inverse of a probability distribution can lead to exact and very fast methods for generating random variables, if the approximation is made exact by adjusting the argument of the approximating function. This article describes the basic method and extensions of it. It gives four examples, of which two are methods for generating gamma- and t-variates that, while meant to illustrate the basic method, show promise of being faster than the best current methods.