Asymptotically Optimal Design Points for Rejection Algorithms |
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Authors: | Gerhard Derflinger Wolfgang Hörmann |
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Institution: | 1. Institut für Statistik und Mathematik, Wirtschaftsuniversit?t Wien , Wien, Austria derfling@statistik.wu-wien.ac.at;3. Institut für Statistik und Mathematik, Wirtschaftsuniversit?t Wien , Wien, Austria |
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Abstract: | ABSTRACT Very fast automatic rejection algorithms were developed recently which allow us 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. Therefore, we present an approach that allows us 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. |
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Keywords: | Optimal design points Random variate generation Rejection method Transformed density rejection |
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