Fitting bivariate losses with phase-type distributions

Amin Zadeh and Martin Bilodeau

Scandinavian Actuarial Journal, 2013, vol. 2013, issue 4, 241-262

Abstract: Maximum likelihood estimation and (parametric bootstrap) goodness-of-fit test are considered for bivariate phase-type distributions introduced by Assaf and Colleagues. In a special case, the dependence structure of bivariate phase-type distributions is revealed. The results are used to fit a real bi-dimensional data set related to insurance losses (LOSS) and allocated loss adjustment expenses (ALAE). The fitted bivariate phase-type is used to obtain conditional quantiles and mean of ALAE for a given value of LOSS. The bivariate phase-type distribution meets all the requirements listed in the study by Klugman and Parsa.

Date: 2013
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DOI: 10.1080/03461238.2011.602196

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