Estimating L -functionals for heavy-tailed distributions and application

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. copyright © 2010 a. necir and d. meraghni.