When modelling insurance claim count data, the actuary often observes overdispersion and an excess of zeros that may be caused by unobserved heterogeneity. A common approach to accounting for overdispersion is to consider models with some overdispersed distribution as opposed to Poisson models. Zero-inflated, hurdle and compound frequency models are typically applied to insurance data to account for such a feature of the data. However, a natural way to deal with unobserved heterogeneity is to consider mixtures of a simpler models. In this paper, we consider k
-finite mixtures of some typical regression models. This approach has interesting features: first, it allows for overdispersion and the zero-inflated model represents a special case, and second, it allows for an elegant interpretation based on the typical clustering application of finite mixture models. k
-finite mixture models are applied to a car insurance claim dataset in order to analyse whether the problem of unobserved heterogeneity requires a richer structure for risk classification. Our results show that the data consist of two subpopulations for which the regression structure is different.
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