92-12-04.wh
#
New Generators of Normal and Poisson Deviates
Based on the Transformed Rejection Method

### Abstract

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