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Quantile Inequalities for the Expectations of Generalized L-Statistics

It is well known that if Xr: n and Yr: n are order statistics from the i.i.d. samples with distribution functions F and G, respectively, such that F succeeds G in the convex order then . The result was extended to the generalized order statistics, and is also valid for their convex combinations. In this paper, we show that analogous relations hold true for much larger classes of linear combinations of generalized order statistics.