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On the Analysis of the Truncated Generalized Poisson Distribution Using a Bayesian Method

Published online by Cambridge University Press:  29 August 2014

David P.M. Scollnik
David P.M. Scollnik*
Affiliation:
Department of Mathematics and Statistics, University of Calgary
*
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canadascollnik@acs.ucalgary.ca
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Abstract

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The generalized Poisson distribution with parameters θ and λ was introduced by Consul and Jain (1973) and has recently found several instances of application in the actuarial literature. The most frequently used version of the distribution assumes that θ > 0 and 0 ≤ λ < 1, in which case the mean and variance are θ/(1 − λ) and θ/(1 − λ)3, respectively. These simple moment expressions, along with nearly all of the other theoretical results available for this distribution, fail when λ < 0 or λ > 1 (e.g., Johnson, Kotz, and Kemp, 1992, page 397). In these cases, even the definition of the probability mass function usually given in the literature is not properly normalized so that its values do not sum to unity. For this reason, it is common to truncate the support of the distribution and explicitly normalize the probability mass function. In this paper we discuss the estimation of the parameters of this truncated generalized Poisson distribution using a Bayesian method.

Keywords

Bayesianbivariategeneralized PoissonLangrangian PoissontruncatedMarkov chain Monte Carlo
Type
Workshops
Information
ASTIN Bulletin: The Journal of the IAA , Volume 28 , Issue 1 , May 1998 , pp. 135 - 152
Copyright
Copyright © International Actuarial Association 1998

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