Bounds for Expectations of Differences of Generalized Order Statistics Based on General and Life Distributions

Let X _? ^(r), r ≥ 1, denote generalized order statistics based on an arbitrary distribution function F with finite pth absolute moment for some 1 ≤ p ≤ ∞. We present sharp upper bounds on E(X _? ^(s) ? X _? ^(r)), 1 ≤ r < s, for F being either general or life distribution. The bounds are expressed in various scale units generated by pth central absolute or raw moments of F, respectively. The distributions achieving the bounds are specified.