Abstract

: We give an algorithm that can be used to sample from any discrete log-concave distribution (e.g. the binomial and hypergeometric distributions). It is based on rejection from a discrete dominating distribution that consists of parts of the geometric distribution. The algorithm is uniformly fast for all discrete log-concave distributions and not much slower than algorithms designed for a single distribution. AMS Subject Classification: 65C10, 68C25. Key Words: Random number generation, log-concave distributions, rejection method, simulation. 1. Introduction A discrete distribution on the integers is called log-concave if the probabilities p k satisfy p 2 k p k\Gamma1 p k+1 for all k. Most of the classical discrete distributions like the binomial, Poisson, negative binomial and hypergeometric distributions are of this type (the only non log-concave distribution that has a chapter of its own in [9] is the logarithmic series distribution). Among the less often used log-concave di...

Citations