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Journal of Probability and Statistics
Volume 2010, Article ID 707146, 34 pages
Research Article

Estimating 𝐿 -Functionals for Heavy-Tailed Distributions and Application

Laboratory of Applied Mathematics, Mohamed Khider University of Biskra, 07000 Biskra, Algeria

Received 5 October 2009; Accepted 21 January 2010

Academic Editor: Ričardas Zitikis

Copyright © 2010 Abdelhakim Necir and Djamel Meraghni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


𝐿 -functionals summarize numerous statistical parameters and actuarial risk measures. Their sample estimators are linear combinations of order statistics ( 𝐿 -statistics). There exists a class of heavy-tailed distributions for which the asymptotic normality of these estimators cannot be obtained by classical results. In this paper we propose, by means of extreme value theory, alternative estimators for 𝐿 -functionals and establish their asymptotic normality. Our results may be applied to estimate the trimmed 𝐿 -moments and financial risk measures for heavy-tailed distributions.