A bivariate model of claim frequencies and severities

Authors: Escarela, Gabriel; Carriére, Jacques F.

Source: Journal of Applied Statistics, Volume 33, Number 8, September 2006 , pp. 867-883(17)

Publisher: Routledge, part of the Taylor & Francis Group

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Abstract:

<p>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.</p>

Keywords: Bivariate loss distribution; Frank's copula; Survival copula; Burr regression; Diagnostics

Document Type: Research article

DOI: http://dx.doi.org/10.1080/02664760600743969

Affiliations: 1: Departamento de Matematicas, Universidad Autonoma Metropolitana, Mexico

Publication date: 2006-09-01

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