Abstract
Abstract The basic distributional properties and estimation techniques of the Poisson-Inverse Gaussian (P-IG) distribution are reviewed. Its use both as a mixed and compound claim frequency model are also discussed, as well as a review of the aggregate claims distribution when the P-IG is the claim frequency component. The many properties which are analogous to those of the negative binomial are emphasized, and the superior fit to automobile claim frequency data is demonstrated. The P-IG merits consideration as a model for claim frequency data due to its good fit to data, physical justification, and its abundance of convenient mathematical properties.
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