Modeling Insurance Claim Distribution via Mixture Distribution and Copula

This paper analyses whether joint probability distribution function of losses due to different exposures covered under the same policy could be modeled in an appropriate manner via mixture distribution proposed and copula concept.
Special type of distribution which is a mixture of Generalized Hyperbolic Skew t distribution and Extreme Value theory (EVT) has been used for modeling marginal distributions of claims and copula function has been considered as a means of modeling dependency structure among claims. Most important copula including; Gaussian, t, Frank, Gumbel and Clayton was tested from goodness of fit point of view.
The data used in this study are the amount of property damage and bodily injury covered under automobile liability insurance.
Results reveal that joint probability distribution of claims could be effectively modeled by Clayton copula and proposed mixture distribution.