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Actuarial statistics with generalized linear mixed models. (English) Zbl 1104.62111

Summary: Over the last decade the use of generalized linear models (GLMs) in actuarial statistics has received a lot of attention, starting from the actuarial illustrations in the standard text by P. McCullagh and J. A. Nelder [Generalized linear models. 2nd ed. (1989; Zbl 0744.62098)]. Traditional GLMs, however, model a sample of independent random variables. Since actuaries very often have repeated measurements or longitudinal data (i.e., repeated measurements over time) at their disposal, this article considers statistical techniques for modelling such data within the framework of GLMs.
Use is made of generalized linear mixed models (GLMMs) which model a transformation of the mean as a linear function of both fixed and random effects. Likelihood and Bayesian approaches to GLMMs are explained. The models are illustrated by considering classical credibility models and more general regression models for non-life ratemaking in the context of GLMMs. Details on computation and implementation (in SAS and WinBugs) are provided.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
65C60 Computational problems in statistics (MSC2010)
62J12 Generalized linear models (logistic models)
91B30 Risk theory, insurance (MSC2010)

Citations:

Zbl 0744.62098

Software:

SAS; WinBUGS
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Full Text: DOI

References:

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