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Modelling repeated insurance claim frequency data using the generalized linear mixed model


  • Kelvin Yau
  • Karen Yip
  • H. K. Yuen


Most of the methods used to estimate claim frequency rates in general insurance have assumed that data are independent. However, it is not uncommon for information stored in the database of an insurance company to contain previous years' claim data from each policyholder. We consider the application of the generalized linear mixed model approach to the analysis of repeated insurance claim frequency data in which a conditionally fixed random effect vector is incorporated explicitly into the linear predictor to model the inherent correlation. A motor insurance data set is used as the basis for simulation to demonstrate the advantages of the method. Ignoring the underlying association for observations within the same policyholder results in an underestimation of the standard error of the parameter estimates and a remarkable reduction in the prediction accuracy. The method provides a viable alternative for incorporating repeated claim experience that enables the revision of rates in general insurance.

Suggested Citation

  • Kelvin Yau & Karen Yip & H. K. Yuen, 2003. "Modelling repeated insurance claim frequency data using the generalized linear mixed model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(8), pages 857-865.
  • Handle: RePEc:taf:japsta:v:30:y:2003:i:8:p:857-865
    DOI: 10.1080/0266476032000075949

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    References listed on IDEAS

    1. Dionne, Georges & Vanasse, Charles, 1989. "A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 19(02), pages 199-212, November.
    2. Renshaw, Arthur E., 1994. "Modelling the Claims Process in the Presence of Covariates," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 24(02), pages 265-285, November.
    3. K. K. W. Yau, 1999. "Estimation of surgeon effects in the analysis of post-operative colorectal cancer patients data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(2), pages 257-272.
    4. Stroinski, Krzysztof J. & Currie, Iain D., 1989. "Selection of variables for automobile insurance rating," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 35-46, March.
    5. Kelvin K. W. Yau & Anthony Y. C. Kuk, 2002. "Robust estimation in generalized linear mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 101-117.
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    Cited by:

    1. GÓMEZ GARCÍA, J.Mª & PELÁEZ FERMOSO, F.J. & y GARCÍA GONZÁLEZ, A., 2005. "Repercusiones del envejecimiento demográfico sobre el sistema público de pensiones en Castilla y León," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 23, pages 235-253, Abril.

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