An expectation-maximization algorithm for the exponential-generalized inverse gaussian regression model with varying dispersion and shape for modelling the aggregate claim amount

This article presents the Exponential–Generalized Inverse Gaussian regression model with varying dispersion and shape. The EGIG is a general distribution family which, under the adopted modelling framework, can provide the appropriate level of flexibility to fit moderate costs with high frequencies and heavy-tailed claim sizes, as they both represent significant proportions of the total loss in non-life insurance. The model’s implementation is illustrated by a real data application which involves fitting claim size data from a European motor insurer. The maximum likelihood estimation of the model parameters is achieved through a novel Expectation Maximization (EM)-type algorithm that is computationally tractable and is demonstrated to perform satisfactorily.