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Dispersion Estimates for Poisson and Tweedie Models

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  • Rosenlund, Stig

Abstract

As a consequence of pointing out an ambiguity in Renshaw (1994), we show that the Overdispersed Poisson model cannot be generated by random independent intensities. Hence Pearson's chi-square-based estimate is normally unsuitable for GLM (Generalized Linear Model) log link claim frequency analysis in insurance. We propose a new dispersion parameter estimate in the GLM Tweedie model for risk premium. This is better than the Pearson estimate, if there are sufficiently many claims in each tariff cell. Simulation results are given showing the differences between it and the Pearson estimate.

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  • Rosenlund, Stig, 2010. "Dispersion Estimates for Poisson and Tweedie Models," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 271-279, May.
    • Handle: RePEc:cup:astinb:v:40:y:2010:i:01:p:271-279_00
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    Cited by:

    1. Denuit, Michel & Trufin, Julien, 2016. "Beyond the Tweedie Reserving Model: The Collective Approach to Loss Development," LIDAM Discussion Papers ISBA 2016030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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