92-04-13.wh

# The Transformed Rejection Method for Generating Poisson Random Variables

## Wolfgang Hörmann

### Abstract

The transformed rejection method, a combination of the inversion and the rejection method, which is used to generate non-uniform random numbers from a variety of continuous distributions can be applied to discrete distributions as well. For the Poisson distribution a short and simple algorithm is obtained which is well suited for large values of the Poisson parameter $\mu$, even when $\mu$ may vary from call to call. The average number of uniform deviates required is lower than for any of the known uniformly fast algorithms. Timings for a C implementation show that the algorithm needs only half of the code but is - for $\mu$ not too small - at least as fast as the current state-of-the-art algorithms.

Mathematics Subject Classification: 65C10 (Random Number Generation)

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

Key Words: rejection method, inversion, decomposition, Poisson variate generation, uniformly fast algorithm

Wolfgang.Hoermann@statistik.wu-wien.ac.at