Estimating L-functionals for heavy-tailed distributions and application (Q609711)

Summary: \(L\)-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. 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.