Asymptotically Optimal Design Points for Rejection Algorithms

Gerhard Derflinger and Wolfgang Hörmann


Very fast automatic rejection algorithms were developed recently which allow to generate random variates from large classes of unimodal distributions. They require the choice of several design points which decompose the domain of the distribution into small sub-intervals. The optimal choice of these points is an important but unsolved problem. So we present an approach that allows to characterize optimal design points in the asymptotic case (when their number tends to infinity) under mild regularity conditions. We describe a short algorithm to calculate these asymptotically optimal points in practice. Numerical experiments indicate that they are very close to optimal even when only six or seven design points are calculated.

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: nonuniform random variate generation, universal algorithm, transformed density rejection, optimal design points

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