Duration dependence models for claim counts

The aim of the paper is to introduce new claim count distributions constructed from different waiting time assumptions, such as the Exponential, Gamma and Weibull distributions. These models are then fitted to panel data with Gamma distributed random effects. The random effects allow for serial dependence and take residual heterogeneity into account. Predictive distributions are obtained with the help of Markov Chain Monte Carlo simulations. The approach is illustrated on the basis of a Belgian motor third party liability insurance portfolio observed for three years.