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Full Credibility with Generalized Linear and Mixed Models

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  • Garrido, José
  • Zhou, Jun

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.

Suggested Citation

  • Garrido, José & Zhou, Jun, 2009. "Full Credibility with Generalized Linear and Mixed Models," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 61-80, May.
    • Handle: RePEc:cup:astinb:v:39:y:2009:i:01:p:61-80_00
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    Cited by:

    1. Alicja Wolny-Dominiak & Tomasz Żądło, 2021. "The Measures of Accuracy of Claim Frequency Credibility Predictor," Sustainability, MDPI, vol. 13(21), pages 1-13, October.
    2. Jonathan Mwau Mulwa, 2018. "Sectoral credit diversification, bank performance and monitoring effectiveness; a cross-country analysis of east African banking industries," Journal of Finance and Investment Analysis, SCIENPRESS Ltd, vol. 7(2), pages 1-2.
    3. Meng Sun & Yi Lu, 2022. "A Generalized Linear Mixed Model for Data Breaches and Its Application in Cyber Insurance," Risks, MDPI, vol. 10(12), pages 1-23, November.

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