Abstract
Let X 1,…, X n be i.i.d. random variables with finite pth absolute moment and X 1:n ,…, X n:n denote the order statistics. We derive sharp upper bounds for E(X k:n − X j:n ), 1 ≤ j < k ≤ n, in different scale units generated by various central absolute moments of a single observation. We also determine the distribution functions for which the bounds are achieved.
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