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Dispersion Estimates for Poisson and Tweedie Models

Published online by Cambridge University Press:  09 August 2013

Stig Rosenlund
Stig Rosenlund*
Affiliation:
Västmannagatan 93, S-113 43 Stockholm, Sweden, E-mail: [email protected]
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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.

Keywords

Generalized Linear ModelGLM log linkODPOverdispersed PoissonTweedie
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 271 - 279
Copyright
Copyright © International Actuarial Association 2010

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References

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