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EM Algorithm for Mixed Poisson and Other Discrete Distributions

Published online by Cambridge University Press:  17 April 2015

Dimitris Karlis
Dimitris Karlis*
Affiliation:
Department of Statistics, Athens University of Economics and Business, 76, Patission str, 10434, Athens, Greece. Email: karlis@aueb.gr
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Abstract

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Mixed Poisson distributions are widely used in various disciplines including actuarial applications. The family of mixed Poisson distributions contains several members according to the choice of the mixing distribution for the parameter of the Poisson distribution. Very few of them have been studied in depth, mainly because of algebraic intractability. In this paper we will describe an EM type algorithm for maximum likelihood estimation for mixed Poisson distributions. The main achievement is that it reduces the problem of estimation to one of estimation of the mixing distribution which is usually easier. Variants of the algorithm work even when the probability function of the mixed distribution is not known explicitly but we have only an approximation of it. Other discrete distributions are treated as well.

Keywords

Poisson mixturesbeta-binomial distributionYule distributionMonte Carlo EM
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 35 , Issue 1 , May 2005 , pp. 3 - 24
Copyright
Copyright © ASTIN Bulletin 2005

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