Author:
Ambagaspitiya R.S.,Balakrishnan N.
Abstract
AbstractGoovaerts 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.
Publisher
Cambridge University Press (CUP)
Subject
Economics and Econometrics,Finance,Accounting
Reference14 articles.
1. Evaluating Compound Generalized Poisson Distributions Recursively
2. Maximum likelihood estimation for the generalized Poisson distribution;Consul;Communications in Statistics- Theory and Methods,1984
3. Use of Lagrange Expansion for Generating Discrete Generalized Probability Distributions
4. A model for distributions of injuries in auto-accidents;Consul;Itteilungen der Schweiz Vereinigung der Versicherungsmathematiker,1990
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