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A representation for discrete distributions by equiprobable mixtures

Published online by Cambridge University Press:  14 July 2016

Arthur V. Peterson Jr. and
Richard A. Kronmal
Arthur V. Peterson Jr.*
Affiliation:
University of Washington and Fred Hutchinson Cancer Research Center
Richard A. Kronmal*
Affiliation:
University of Washington
*
∗ Postal address: Department of Biostatistics, SC–32, University of Washington, Seattle, WA 98195, U.S.A.
∗ Postal address: Department of Biostatistics, SC–32, University of Washington, Seattle, WA 98195, U.S.A.
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Abstract

We obtain a representation of an arbitrary discrete distribution with n mass points by an equiprobable mixture of r distributions, each of which has no more than a (≧2) mass points, where r is the smallest integer greater than or equal to (n – 1)/(a – 1). An application to the generation of discrete random variables on a computer is described, which has as an important special case Walker's (1977) alias method.

Keywords

REPRESENTATIONSDISCRETE DISTRIBUTIONEQUIPROBABLE MIXTURERANDOM NUMBER GENERATIONMONTE CARLOALIAS METHOD

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980, pp. 102 - 111
Copyright
Copyright © Applied Probability Trust 1980 

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References

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