Estimation of Parametric and Nonparametric Models for Univariate Claim Severity Distributions - an approach using R
AbstractThis 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.
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Bibliographic InfoPaper provided by Xarxa de Referència en Economia Aplicada (XREAP) in its series Working Papers with number XREAP2011-06.
Length: 48 pages
Date of creation: Jun 2011
Date of revision: Jun 2011
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Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques i Empresarials, Universitat de Barcelona, c/ Tinent Coronel Valenzuela, 1-11, 08034 Barcelona
Web page: http://www.pcb.ub.edu/xreap
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