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A large claim index. (English) Zbl 0766.62061

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)

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B82 Statistical methods; economic indices and measures
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