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A bivariate model of claim frequencies and severities

Author

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  • Drgabriel Escarela
  • Jacques Carriere

Abstract

Bivariate claim data come from a population that consists of insureds who may claim either one, both or none of the two types of benefits covered by a policy. In the present paper, we develop a statistical procedure to fit bivariate distributions of claims in presence of covariates. This allows for a more accurate study of insureds' choice and size in the frequency and severity of the two types of claims. A generalised logistic model is employed to examine the frequency probabilities, whilst the three parameter Burr distribution is suggested to model the underlying severity distributions. The bivariate copula model is exploited in such a way that it allows us to adjust for a range of frequency dependence structures; a method for assessing the adequacy of the fitted severity model is outlined. A health claims dataset illustrates the methods; we describe the use of orthogonal polynomials for characterising the relationship between age and the frequency and severity models.

Suggested Citation

  • Drgabriel Escarela & Jacques Carriere, 2006. "A bivariate model of claim frequencies and severities," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(8), pages 867-883.
    • Handle: RePEc:taf:japsta:v:33:y:2006:i:8:p:867-883
    DOI: 10.1080/02664760600743969
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    Cited by:

    1. Zhao, Xiaobing & Zhou, Xian, 2012. "Copula models for insurance claim numbers with excess zeros and time-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 191-199.

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