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Non-parametric Models for Univariate Claim Severity Distributions - an approach using R

Author

Listed:
  • Catalina Bolance

    () (Department of Econometrics, Riskcenter-IREA, Universitat de Barcelona)

  • Montserrat Guillen

    () (Department of Econometrics, Riskcenter-IREA, Universitat de Barcelona)

  • David Pitt

    () (Department of Applied Finance and Actuarial Studies, Macquarie University)

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 esti- mated with non-parametric methods. The methods are implemented using the statistical package R. 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

  • Catalina Bolance & Montserrat Guillen & David Pitt, 2014. "Non-parametric Models for Univariate Claim Severity Distributions - an approach using R," Working Papers 2014-01, Universitat de Barcelona, UB Riskcenter.
  • Handle: RePEc:bak:wpaper:201401
    as

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    File URL: http://www.ub.edu/rfa/research/WP/UBriskcenterWP201401.pdf
    File Function: First version, 2014
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    References listed on IDEAS

    as
    1. Hall, Peter & Marron, J. S., 1987. "Estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 109-115, November.
    2. 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.
    3. 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.
    4. 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.
    5. Vernic, Raluca, 2006. "Multivariate skew-normal distributions with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 413-426, April.
    6. Marco Corazza & Florence Legros & Cira Perna & Marilena Sibillo, 2017. "Mathematical and Statistical Methods for Actuarial Sciences and Finance," Post-Print hal-01776135, HAL.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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    Cited by:

    1. Estefanía Alaminos & Mercedes Ayuso, 2015. "Methodological Approach of a Multiple State Actuarial Model for the Married - Widower case for the assessment of retirement and widowhood pensions," Working Papers 2015-04, Universitat de Barcelona, UB Riskcenter.

    More about this item

    Keywords

    Loss modeling; insurance; finance;

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