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Document Details :
Title: Recursive Formulas for Compound Phase Distributions
Subtitle: Univariate and Bivariate Cases
Author(s): REN, Jiandong
Journal: ASTIN Bulletin
Volume: 40 Issue: 2 Date: 2010
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.