Estimation of Parametric and Nonparametric Models for Univariate Claim Severity Distributions: An Approach Using R

XREAP No. 2011-06

48 Pages Posted: 3 Jun 2011

See all articles by David Pitt

David Pitt

University of Melbourne - Department of Economics

Montserrat Guillen

Catalina Bolancé

University of Barcelona - Department of Econometrics

Date Written: May 19, 2011

Abstract

This paper presents an analysis of motor vehicle insurance claims relating to vehicle damage and to associated medical expenses. We use univariate severity distributions estimated with parametric and non-parametric methods. The methods are implemented using the statistical package R. Parametric analysis is limited to estimation of normal and lognormal distributions for each of the two claim types. The nonparametric analysis presented involves kernel density estimation. We illustrate the benefits of applying transformations to data prior to employing kernel based methods. We use a log-transformation and an optimal transformation amongst a class of transformations that produces symmetry in the data. The central aim of this paper is to provide educators with material that can be used in the classroom to teach statistical estimation methods, goodness of fit analysis and importantly statistical computing in the context of insurance and risk management. To this end, we have included in the Appendix of this paper all the R code that has been used in the analysis so that readers, both students and educators, can fully explore the techniques described.

Suggested Citation

Pitt, David and Guillen, Montserrat and Bolancé, Catalina, Estimation of Parametric and Nonparametric Models for Univariate Claim Severity Distributions: An Approach Using R (May 19, 2011). XREAP No. 2011-06. Available at SSRN: https://ssrn.com/abstract=1856982 or http://dx.doi.org/10.2139/ssrn.1856982

David Pitt (Contact Author)

University of Melbourne - Department of Economics ( email )

Melbourne, 3010
Australia

Catalina Bolancé

University of Barcelona - Department of Econometrics ( email )

Av. Diagonal 690
Barcelona, E-08034
Spain

No contact information is available for Montserrat Guillen

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