Aebi, Markus; Embrechts, Paul; Mikosch, Thomas A large claim index. (English) Zbl 0766.62061 Mitt., Schweiz. Ver. Versicherungsmath. 1992, No. 2, 143-156 (1992). Given an ordered sample, \(Y_ 1,Y_ 2,\dots,Y_ n\), drawn from a distribution \(F\) with finite expectation, \(\mu\), the authors define an index which measures the relative contribution the sum of largest values makes to the sample mean: the index is \(\mu^{-1}\int^ 1_ \alpha F^{-1}(x)dx\). Before presenting a table of some values of the index for selected members of the Pareto family and the exponential and graphs of these as well as of loggamma, lognormal and gamma, the authors demonstrate the index is the almost sure limit, as \(n\to\infty\), of the ratio \((Y_{[n\alpha]}+\cdots+Y_ n)/(Y_ 1+\cdots+Y_ n)\). Reviewer: G.Lord (Princeton) Cited in 4 Documents MSC: 62P05 Applications of statistics to actuarial sciences and financial mathematics 91B82 Statistical methods; economic indices and measures Keywords:large claims; Lorenz curve; exponential distributions; ordered sample; finite expectation; sum of largest values; sample mean; table; Pareto family; loggamma; lognormal; gamma PDFBibTeX XMLCite \textit{M. Aebi} et al., Mitt., Schweiz. Ver. Versicherungsmath. 1992, No. 2, 143--156 (1992; Zbl 0766.62061)