We present sharp bounds for an approximation of fractional kth record values by convex combinations of ordinary kth record values. The bounds are ex-pressed in different scale units measured in pth central absolute moments of the under-lying distribution. The distributions which attain the bounds are also specified. The bounds are derived by the projection method.
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We present sharp bounds for expectations of generalized order statistics with random indices expressed in terms of Tsallis’ entropy. The bounds are attainable and provide new characterizations of some nontrivial distributions. No restrictions are imposed on the parameters of the generalized order statistics model.
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