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Recursive Formulas for Compound Phase Distributions – Univariate and Bivariate Cases

Published online by Cambridge University Press:  09 August 2013

Jiandong Ren
Jiandong Ren*
Affiliation:
Department of Statistical and Actuarial Sciences, University of Western Ontario, 1150 Richmond Street North, Western Science Centre, Room 262, London, Ontario, N6A 5B7, Canada. Tel: 001-(519) 661-2111 Ext. 88209, Fax: (519) 661-3813, E-Mail: [email protected]
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Abstract

We first present a simple matrix-based recursive formula for calculating the distribution function of compound phase-type random variables. Then we extend the results to the case when the number of claims follows a bivariate matrix negative binomial (BMNB) distribution detailed herein. Further, extending the results in Hipp (2006), we provide speedy recursive formulas for both the univariate and the bivariate models when the claim sizes follow discrete phase-type distributions. Numerical examples are provided.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 2 , November 2010 , pp. 615 - 629
Copyright
Copyright © International Actuarial Association 2010

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