Modelling losses using an exponential-inverse Gaussian distribution

An exponential-inverse Gaussian distribution is used to model the claim size distribution. The distribution has shorter tails than the Pareto distribution and it is considered as a plausible model for data without large tails. We present the model allowing for covariates. Properties of the model are discussed. An EM algorithm is provided to fit the model. The algorithm is quite simple and programmable without need for any special functions. The model can be seen as a random effect model for exponential survival times regression. A real data application using a car-insurance company portfolio data is provided.