New Generators of Normal and Poisson Deviates Based on the Transformed Rejection Method

Wolfgang Hörmann


The transformed rejection method uses inversion to sample from the dominating density of a rejection algorithm. But in contrast to the usual method it is enough to know the inverse distribution function $F^{-1}(x)$ of the dominating density. This idea can be applied to various continuous (e.g. normal, Cauchy and exponential) and discrete (e.g. binomial and Poisson) distributions with high acceptance probabilities. The resulting algorithms are short, simple and fast. Even more important is the fact that the quality of the method when used in combination with a linear congruential uniform generator is high compared with the quality of the ratio of uniforms method. In addition transformed rejection can be easily employed for correlation induction.

Mathematics Subject Classification: 65C10 (Random Number Generation)

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

Key Words: random variate generation, rejection method

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