Garrido, Jose and Zhou, Jun (2006) Credibililty Theory for Generalized Linear and Mixed Models. Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.
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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.
| Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
|---|---|
| Item Type: | Monograph (Technical Report) |
| Authors: | Garrido, Jose and Zhou, Jun |
| Series Name: | Department of Mathematics & Statistics. Technical Report No. 5/06 |
| Corporate Authors: | Concordia University. Department of Mathematics & Statistics |
| Institution: | Concordia University |
| Date: | December 2006 |
| Keywords: | GLMs, GLMMs, limited fluctuations credibility, confidence intervals |
| ID Code: | 6676 |
| Deposited By: | DIANE MICHAUD |
| Deposited On: | 03 Jun 2010 20:49 |
| Last Modified: | 18 Jan 2018 17:29 |
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