Kernel Density Estimation for Heavy-Tailed Distributions Using the Champernowne Transformation

32 Pages Posted: 22 Apr 2005

See all articles by Tine Buch-Kromann

Tine Buch-Kromann

Royal & SunAlliance

Jens Perch Nielsen

City University London - Cass Business School

Montserrat Guillen

Catalina Bolancé

University of Barcelona - Department of Econometrics

Date Written: January 2005

Abstract

When estimating loss distributions in insurance, large and small losses are usually split because it is difficult to find a simple parametric model that fits all claim sizes. This approach involves determining the threshold level between large and small losses. In this article a unified approach to the estimation of loss distributions is presented. We propose an estimator obtained by transforming the data set with a modification of the Champernowne cdf and then estimating the density of the transformed data by use of the classical kernel density estimator. We investigate the asymptotic bias and variance of the proposed estimator. In a simulation study, the proposed method shows a good. performance. We also present two applications dealing with claims costs in insurance.

Keywords: Actuarial loss models, Transformation, Skewness, Champernowne distribution, Extreme Value Theory

Suggested Citation

Buch-Kromann, Tine and Nielsen, Jens Perch and Guillen, Montserrat and Bolancé, Catalina, Kernel Density Estimation for Heavy-Tailed Distributions Using the Champernowne Transformation (January 2005). Available at SSRN: https://ssrn.com/abstract=704903 or http://dx.doi.org/10.2139/ssrn.704903

Tine Buch-Kromann (Contact Author)

Royal & SunAlliance ( email )

Gammel Kongevej 60
DK-1790 Copenhagen
Denmark

Jens Perch Nielsen

City University London - Cass Business School ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Catalina Bolancé

University of Barcelona - Department of Econometrics ( email )

Av. Diagonal 690
Barcelona, E-08034
Spain

No contact information is available for Montserrat Guillen