Computer methods for efficient sampling from largely arbitrary statistical distributions

Given a basic pseudo-random number generator which returns uniformly distributed samplesU from the interval (0, 1) and a statistical distribution as defined by its distribution functionF(x). Then the inversion methodX←F ^?1 (U) produces samples fromF(x). A procedure is developed which prepares “guide tables” in order to facilitate this inversion so that sampling becomes efficient for arbitraryF(x). For discrete distributions these tables are small and easy to set up, and the resulting sampling algorithm compares well with known general methods. Continuous distributions require longer set-up times and more space for tables. These are prepared using given probability densitiesf(x). The method can cope with “reasonable”f(x) including most cases which are commonly encountered in statistics. The reported computational experience, on Poisson, Normal, Gamma and Cauchy distributions, indicates that our general routine is almost as fast as the best known sampling algorithms which were specially designed for these distributions.