Kernel density estimation for heavy-tailed distributions using the champernowne transformation

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...

Full description

Saved in:
Bibliographic Details
Published inStatistics (Berlin, DDR) Vol. 39; no. 6; pp. 503 - 516
Main Authors Buch-larsen, Tine, Nielsen, Jens Perch, Guillén, Montserrat, Bolancé, Catalina
Format Journal Article
LanguageEnglish
Published Taylor & Francis 01.12.2005
Subjects
Actuarial loss models
Champernowne distribution
Skewness
Transformation
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0233-1888
1029-4910
DOI:10.1080/02331880500439782