ARVAG - Automatic nonuniform Random VAriate Generation |

Project |

**Project**

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 methodand the method ofindexed 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

- Design of universal generators for multivariate distributions.
- Algorithms with fast setup.
- Improved generators in the framework of Markov chain Monte Carlo methods.
- Fast methods for creating nonuniform quasi-random numbers (a sequence with low F-discrepancy, i.e. where the deviation of the empirical distribution function from the theoretical distribution function tends to zero).
- Investigate the quality of the resulting nonuniform pseudo-random variates.
- Generating multidimensional variates from data.
- Building of a reliable and portable C library for all important automatic generators.

Gerhard Derflinger Wolfgang Hörmann Josef Leydold Günter Tirler

Former team members:

Erich Janka

Project |

Wolfgang Hörmann and Josef Leydold (October 21st, 2003) | Research supported by |