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An introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions

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  • David Pitt

    ()
    (Dept. Economics, University of Melbourne)

  • Montserrat Guillén

    ()
    (Dept. Econometrics, University of Barcelona)

Abstract

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.

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File URL: http://www.pcb.ub.es/xreap/aplicacio/fitxers/XREAP2010-3.pdf
File Function: First version, 2010
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File URL: http://www.pcb.ub.es/xreap/aplicacio/fitxers/XREAP2010-3.pdf
File Function: Revised version, 2010
Download Restriction: no

Bibliographic Info

Paper provided by Xarxa de Referència en Economia Aplicada (XREAP) in its series Working Papers with number XREAP2010-03.

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Length: 25 pages
Date of creation: Mar 2010
Date of revision: Mar 2010
Handle: RePEc:xrp:wpaper:xreap2010-03

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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
Phone: +34+934039653
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Web page: http://www.pcb.ub.edu/xreap
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  1. 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.
  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. 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.
  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. 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.
  6. 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.
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Cited by:
  1. Ramon Alemany & Catalina Bolancé & Montserrat Guillén, 2012. "Nonparametric estimation of Value-at-Risk," Working Papers XREAP2012-19, Xarxa de Referència en Economia Aplicada (XREAP), revised Oct 2012.

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