92-04-13.wh
#
The Transformed Rejection Method
for Generating Poisson Random Variables

### 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

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