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Sampling from binomial and poisson distributions: A method with bounded computation times

Erzeugung Binomial- und Poisson-verteilter Zufallszahlen: Eine Methode mit beschränkten Rechenzeiten

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Abstract

An accurate acceptance-rejection algorithm is devised and tested. The procedure requires an average of less than 3 uniform deviates whenever the standard deviation σ of the distribution is at least 4, and this number decreases monotonically to 2.63 as σ→∞. Variable parameters are permitted, and no subroutines for sampling from other statistical distributions are needed.

Zusammenfassung

Ein exakter Verwerfungsalgorithmus wird konstruiert und ausgetestet. Das Verfahren erfordert durchschnittlich weniger als 3 gleichverteilte Zufallszahlen, solange die Standardabweichung σ der Verteilung mindestens 4 beträgt; diese Anzahl fällt monoton gegen 2,63 für σ→∞. Variable Parameter sind zugelassen; es werden keinerlei Unterprogramme für Stichproben von anderen statistischen Verteilungen benötigt.

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Authors and Affiliations

  1. Mathematisches Seminar, Universität Kiel, Olshausenstrasse 40-60, D-2300, Kiel, Federal Republic of Germany

    J. H. Ahrens

  2. Institut für Mathematische Statistik, Technische Universität Graz, Hamerlinggasse 6, A-8010, Graz, Austria

    U. Dieter

Authors
  1. J. H. Ahrens
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  2. U. Dieter
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Additional information

This research was supported by the Austrian Research Council (Fonds zur Förderung der wissenschaftlichen Forschung).

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Ahrens, J.H., Dieter, U. Sampling from binomial and poisson distributions: A method with bounded computation times. Computing 25, 193–208 (1980). https://doi.org/10.1007/BF02241999

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  • DOI: https://doi.org/10.1007/BF02241999

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