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Estimation of Parametric and Nonparametric Models for Univariate Claim Severity Distributions - an approach using R

Author

Listed:
  • David Pitt

    () (Department of Applied Finance and Actuarial Studies, Macquarie University, Sydney, New South Wales, 2109 Australia)

  • Montserrat Guillen

    () (RFA-IREA, Departament d’Econometria, Estadística i Economia Espanyola, Avda. Diagonal 690, 08034 Barcelona)

  • Catalina Bolancé

    () (RFA-IREA, Departament d’Econometria, Estadística i Economia Espanyola, Avda. Diagonal 690, 08034 Barcelona)

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

  • David Pitt & Montserrat Guillen & Catalina Bolancé, 2011. "Estimation of Parametric and Nonparametric Models for Univariate Claim Severity Distributions - an approach using R," Working Papers XREAP2011-06, Xarxa de Referència en Economia Aplicada (XREAP), revised Jun 2011.
  • Handle: RePEc:xrp:wpaper:xreap2011-06
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    File URL: http://www.xreap.cat/RePEc/xrp/pdf/XREAP2011-06.pdf
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    File URL: http://www.xreap.cat/RePEc/xrp/pdf/XREAP2011-06.pdf
    File Function: Revised version, 2011
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    References listed on IDEAS

    as
    1. Zhang, Xibin & King, Maxwell L. & Hyndman, Rob J., 2006. "A Bayesian approach to bandwidth selection for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3009-3031, July.
    2. Bolance, Catalina & Guillen, Montserrat & Nielsen, Jens Perch, 2003. "Kernel density estimation of actuarial loss functions," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 19-36, February.
    3. Wu, Tiee-Jian & Chen, Ching-Fu & Chen, Huang-Yu, 2007. "A variable bandwidth selector in multivariate kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 462-467, February.
    4. Bolance, Catalina & Guillen, Montserrat & Pelican, Elena & Vernic, Raluca, 2008. "Skewed bivariate models and nonparametric estimation for the CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 386-393, December.
    5. Qing Liu & David Pitt & Xibin Zhang & Xueyuan Wu, 2010. "A Bayesian approach to parameter estimation for kernel density estimation via transformations," Monash Econometrics and Business Statistics Working Papers 18/10, Monash University, Department of Econometrics and Business Statistics.
    6. Vernic, Raluca, 2006. "Multivariate skew-normal distributions with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 413-426, April.
    7. Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
    8. Hall, Peter & Marron, J. S., 1987. "Estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 109-115, November.
    9. Bolancé, Catalina & Guillén, Montserrat & Nielsen, Jens Perch, 2008. "Inverse beta transformation in kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1757-1764, September.
    10. Clements A. & Hurn S. & Lindsay K., 2003. "Mobius-Like Mappings and Their Use in Kernel Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 993-1000, January.
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    Cited by:

    1. Alghalith, Moawia, 2016. "Novel and simple non-parametric methods of estimating the joint and marginal densities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 454(C), pages 94-98.
    2. Alghalith, Moawia, 2017. "A new parametric method of estimating the joint probability density," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 799-803.
    3. Eling, Martin, 2012. "Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 239-248.

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