2000-03.ley-wh
#
Universal Algorithms as an Alternative for Generating
Non-Uniform Continuous Random Variates

### Abstract

This paper presents an overview of the most
powerful universal methods. These are based on acceptance/rejection
techniques where hat and squeezes are constructed automatically.
Although originally motivated to sample from non-standard
distributions these methods have advantages that make them
attractive even for sampling from standard distributions and thus are
an alternative to special generators tailored for particular distributions.
Most important are: the marginal generation time is fast and does not
depend on the distribution. They can be used for variance reduction
techniques, and they produce random numbers of predictable quality.
These algorithms are implemented in a library, called
UNURAN, which is
available by anonymous ftp.

**Mathematics Subject Classification:**
65C10 (Random Number Generation)

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

**General Terms:**
Algorithms

**Key Words:**
random number generation, rejection method, log-concave density,
transformed density rejection, ratio-of-uniforms, black-box algorithm,
universal method

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Josef.Leydold@statistik.wu-wien.ac.at