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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: stig.rosenlund@sverige.nu
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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

Grigelionis, B. (1963) On the convergence of sums of random step processes to a Poisson process. Probability Theory and its Applications, 8(2), 177–182.Google Scholar
Jørgensen, B. and Paes de Souza, M.C. (1994) Fitting Tweedie’s Compound Poisson Model to insurance claim data. Scandinavian Actuarial Journal, 1994(1), 69–93.Google Scholar
McCullagh, P. and Nelder, J.A. (1989) Generalized linear models, Second Edition. Chapman and Hall, Boca Raton.Google Scholar
Ohlsson, E. and Johansson, B. (2010) Non-Life Insurance Pricing with Generalized Linear Models. Springer.Google Scholar
Parzen, E. (1962) Stochastic Processes. Holden-Day, San Francisco.Google Scholar
Renshaw, A.E. (1994) Modelling the claims process in the presence of covariates. ASTIN Bulletin 24(2), 265–285.Google Scholar
Venter, G.G. (2007) Generalized Linear Models beyond the Exponential Family with Loss Reserve Applications. ASTIN Bulletin 37(2), 345–364.Google Scholar