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Full Credibility with Generalized Linear and Mixed Models

Published online by Cambridge University Press:  09 August 2013

José Garrido  and
Jun Zhou
Jun Zhou
Affiliation:
Research and Development, Aviva Canada Inc., 8th floor, 630 René Lévesque W., Montreal, QC, H3B 1S6, Canada, E-mail: jun_zhou@avivacanada.com
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Abstract

Generalized linear models (GLMs) are gaining popularity as a statistical analysis method for insurance data. For segmented portfolios, as in car insurance, the question of credibility arises naturally; how many observations are needed in a risk class before the GLM estimators can be considered credible? In this paper we study the limited fluctuations credibility of the GLM estimators as well as in the extended case of generalized linear mixed model (GLMMs). We show how credibility depends on the sample size, the distribution of covariates and the link function. This provides a mechanism to obtain confidence intervals for the GLM and GLMM estimators.

Keywords

GLMsGLMMslimited fluctuations credibilityconfidence intervals
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 1 , May 2009 , pp. 61 - 80
Copyright
Copyright © International Actuarial Association 2009

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Footnotes

* This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant 36860–06.

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