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On the Compound Generalized Poisson Distributions

Published online by Cambridge University Press:  29 August 2014

R.S. Ambagaspitiya  and
N. Balakrishnan
R.S. Ambagaspitiya*
Affiliation:
University of Calgary— McMaster University
N. Balakrishnan*
Affiliation:
University of Calgary— McMaster University
*
Department of Mathematics and Statistis, University of Calgary, Calgary, Alberta, CanadaT2N 1N4.
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, CanadaL8S 4K1.
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Abstract

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Goovaerts and Kaas (1991) present a recursive scheme, involving Panjer's recursion, to compute the compound generalized Poisson distribution (CGPD). In the present paper, we study the CGPD in detail. First, we express the generating functions in terms of Lambert's W function. An integral equation is derived for the pdf of CGPD, when the claim severities are absolutely continuous, from the basic principles. Also we derive the asymptotic formula for CGPD when the distribution of claim severity satisfies certain conditions. Then we present a recursive formula somewhat different and easier to implement than the recursive scheme of Goovaerts and Kaas (1991), when the distribution of claim severity follows an arithmetic distribution, which can be used to evaluate the CGPD. We illustrate the usage of this formula with a numerical example.

Keywords

Compound generalized Poisson distributionsmomentsintegral equationsrecursive equationtail behaviour
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 24 , Issue 2 , November 1994 , pp. 255 - 263
Copyright
Copyright © International Actuarial Association 1994

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