Acceptance-Rejection Techniques for Sampling from The Gamma and Beta Distributions.
U. Dieter, Joachim H. Ahrens · 1974
Abstract : John von Neumann's idea of sampling from a distribution by majorizing its probability density function is applied to gamma and beta distributions. Optimum envelopes are constructed resulting in sampling algorithms whose performance will not deteriorate when the parameters are increased. In some methods the process of acceptance is accelerated. For this the employed test functions are replaced in most cases with simpler bounds which are difficult to derive but easy to apply. The reported computational experience indicates that the new methods can be of considerable practical use. (Author)