Universal methods of non-uniform random variate generation.

If only a few random variates are required, methods like adaptive rejection sampling by Gilks and Wild [1992] or rejection from adjusted table-mountain-shaped hat functions (e.

It has become a popular transformation method to generate nonuniform random variates, since it results in exact, efficient, fast, and easy-to-implement algorithms.

Random variate generation by using the ratio-of-uniforms method.

Transformations and random variate generation: Generalised ratio-of-uniforms methods.

Random variates inside the squeeze are generated by mere inversion, and therefore in opposition to any other ratio-of-uniforms method, the expected number of uniform random numbers is less than two.

see Devroye [1986] and Dagpunar [1988]), and in the last years some papers have appeared on automatic (also called universal or black-box) methods (see Devroye [1986, Chapter VII], Gilks and Wild [1992], Ahrens [1995], Hormann [1995], and Hormann and Deflinger [1994]); these are algorithms that can generate random variates from a large family of distributions as long as some information (typically the mode and the density of the specific distribution) are available.

The mathematics necessary for a sweep-plane algorithm to generate uniform random variates over simple polytopes in high dimensions was collected in Leydold and Hormann [1998].

Given a computable, log-concave density f(x, y) and its partial derivatives and the domain of the distribution the algorithm can generate random variates (X, Y) with the desired distribution almost as fast as independent normal pairs can be generated by the Box-Muller method.

Binomial Random Variate Generator," Technical Report, McGill University, Montreal, Quebec, Canada, 1980.

Poisson Random Variate Generation," Research Memorandum 81-4, Purdue University, 1981.

There are many methods for generating random variates from the binomial probability mass function