Automatic random variate generation

Austrian Science Fund

It is readliy accepted in the scientific comunity 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 non-uniform 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 sequential 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:

• Optimize the construction of hat functions for the transformed density method and derive usable properties of the class of T-concave distributions

• Automatic generation of order statistics

• Investigate the quality of the resulting non-uniform pseudo-random variates

• Design universal generators for multivariate distributions

• Generating multidimensional variates from data

• Building of a portable C library for all important automatic generators

• A monography that sumerizes automatic generation techniques

• Applications