ARVAG - Automatic nonuniform Random VAriate Generation


It is readily accepted in the scientific community that simulation is a tool of great and still increasing importance in many fields of research and application. For stochastic simulations the generation of random variates from different distributions is a necessary prerequisite. Thus the first considerations how to generate uniform random numbers and nonuniform random variates started already in the fifties. Since that time hundreds of papers were published proposing algorithms for many important standard distributions, e.g. for the normal, gamma, beta Poisson, and binomial distributions.

For discrete distributions two different automatic (or universal) algorithms, which can be applied to almost all discrete distributions, are well known: the alias method and the method of indexed search.

For automatic algorithms for generating continuous distributions the situation is slightly more difficult. The development in this field was started by Devroye in 1986. A very interesting contribution is due to W. R. Gilks and P.Wild (1992). W. Hörmann (1995) has generalized the concept of Devroye, the corresponding procedure, called transformed density rejection, being applicable to a much larger class of densities, called T-concave densities.

The aims of our project are

About us

Gerhard Derflinger
Wolfgang Hörmann
Josef Leydold
Günter Tirler

Former team members:

Erich Janka

[ARVAG]     Wolfgang Hörmann and Josef Leydold   (October 21st, 2003) Research supported by FWF