Cluster analysis of claim frequency in automobile insurance
When modelling insurance claim counts data, the actuary often observes overdispersion and an excess of zeros that may be caused by unobserved heterogeneity. A common approach for accounting for overdispersion is to consider models with some overdispersed distribution as opposed to Poisson models. Zero-inflated and compound frequency models are usually applied to insurance data to account for such characteristics of the data. However, a natural way to deal with the unobserved heterogeneity is to consider mixtures of a simpler model. In this paper, we consider K-finite mixtures of some usual 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. These models are applied to an automobile insurance claims data set in order to analyse the consequences for risk classification.
Keywords: Zero-inflation Overdispersion Finite mixture regression model
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