Statistics and Computing

, Volume 20, Issue 1, pp 35–55

Beta kernel quantile estimators of heavy-tailed loss distributions

Article

DOI: 10.1007/s11222-009-9114-2

Cite this article as:
Charpentier, A. & Oulidi, A. Stat Comput (2010) 20: 35. doi:10.1007/s11222-009-9114-2

Abstract

In this paper we suggest several nonparametric quantile estimators based on Beta kernel. They are applied to transformed data by the generalized Champernowne distribution initially fitted to the data. A Monte Carlo based study has shown that those estimators improve the efficiency of the traditional ones, not only for light tailed distributions, but also for heavy tailed, when the probability level is close to 1. We also compare these estimators with the Extreme Value Theory Quantile applied to Danish data on large fire insurance losses.

Keywords

Beta kernels Champernowne distribution Loss distributions Quantile estimation Transformed kernel Value-at-risk 

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.CREM-Université Rennes 7Rennes CedexFrance
  2. 2.IMAAngers Cedex 01France