# The transformed rejection method for generating Poisson random variables

Wolfgang Hörmann

Publication: Working/Discussion PaperWU Working Paper

## 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. (author's abstract)
Original language English Vienna Institut für Statistik und Mathematik, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business Published - 1992

### Publication series

Name Preprint Series / Department of Applied Statistics and Data Processing 2

## WU Working Paper Series

• Preprint Series / Department of Applied Statistics and Data Processing