Fitting Tweedie's compound poisson model to insurance claims data

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Abstract
We discuss the estimation and inference problems for the Tweedie compound Poisson process and its application to tarification. For data in the form of the total claim and number of claims for a given time interval and a given exposure, the Tweedie process corresponds to a Poisson process of claims and gamma distributed claim sizes. The model has three parameters, namely the mean claim rate, a dispersion parameter and a shape parameter, and the exposure enters as a weight via the dispersion parameter. The Tweedie process is an exponential dispersion model for fixed value of the shape parameter, and hence regression models for the claim rate may be fitted as in generalized linear models. The shape parameter is estimated by maximum likelihood, and inference is based on the likelihood ratio test, rather than the usual analysis of deviance. A GLIM 4 program for estimation in the model is presented.

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