Rejection-Inversion to Generate Variates from Monotone Discrete Distributions

Wolfgang Hörmann and Gerhard Derflinger


For discrete distributions a variant of rejection from a continuous hat function is presented. The main advantage of the new method, called rejection-inversion, is that no extra uniform random number to decide between acceptance and rejection is required which means that the expected number of uniform variates required is halved. Using rejection-inversion and a squeeze, a simple universal method for a large class of monotone discrete distributions is developed. It can be used to generate variates from the tails of most standard discrete distributions. Rejection-inversion applied to the Zipf (or zeta) distribution results in algorithms that are short and simple and at least twice as fast as the fastest methods suggested in the literature.

Mathematics Subject Classification: 65C10 (Random Number Generation)

CR Categories and Subject Descriptors: G.3 [Probability and Statistics]: Random number generation

General Terms: Algorithms

Key Words: random number generation, rejection method, Zipf distribution, tail of Poisson distribution, universal algorithm, T-concave

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© ACM, (1996). This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Trans. Model. Comput. Simul. 6(3), 169-184. http://doi.acm.org/10.1145/235025.235029