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See detailSmoothed nonparametric maximum likelihood estimation of the risk distribution underlying bonus-malus systems
Denuit, Michel; Lambert, Philippe ULg

in Proceedings of the Casualty Actuarial Society (2001), LXXXVIII

Mixed Poisson distributions are widely used for modeling claim counts when the portfolio is thought to be heterogeneous. The risk (or mixing) distribution then represents a measure of this heterogeneity ... [more ▼]

Mixed Poisson distributions are widely used for modeling claim counts when the portfolio is thought to be heterogeneous. The risk (or mixing) distribution then represents a measure of this heterogeneity. The aim of this paper is to use a variant of the Patilea and Rolin [15] smoothed version of the Simar [20] Non-Parametric Maximum Likelihood Estimator of the risk distribution in the mixed Poisson model. Empirical results based on two data sets from automobile third-party liability insurance demonstrate the relevance of this approach. The design of merit-rating schemes is discussed in the second part of the paper. [less ▲]

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