Extract
Number of Accidents or Number of Claims? An Approach with Zero-Inflated Poisson Models for Panel Data
INTRODUCTION
In various applications involving count data, the data exhibit a high number of zero values. This led to the idea that a distribution with excess zeros can provide a good fit, such as the zero-inflated distribution. In insurance, the hunger for bonus (Philipson, 1960; Lemaire, 1977) is a well-known phenomenon that represents the fact that insureds do not report all their accidents to save bonus on the following year's premium. However, actuaries and researchers continue to model the number of claims with standard count distributions, neglecting the bonus hunger phenomenon. In this article, we assume that the number of accidents is based on a Poisson distribution but that the number of claims is generated by censorship of this Poisson distribution.Risk classification techniques for claim counts have been the topic of many papers in the actuarial literature. Denuit et al. (2007) provides an exhaustive overview of count data models for insurance claims. For cross-sectional data, Boucher, Denuit, and Guillen (2007) studied zero-inflated models in motor insurance-claim counts and compared them to hurdle models. Boucher, Denuit, and Guillen (2008) worked on risk classification models for the number of claims, in the context of panel data but only studied classical count data models, like Poisson and negative binomial. In this article, we propose new zero-inflated models that generalize the distribution for longitudinal data by introducing random effects in the model.We found that the generalizations of the zero-inflated Poisson distribution has interesting applications for insurance data, where the number of accidents can be compared to the number of claims. In "Number of Claims versus Number of Accidents" section, we review the standard techniques used to consider the differences bet...See the full content of this document
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