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Distribution-free bounds on the expectation of the maximum with scheduling applications. (English) Zbl 0715.90068
Summary: Let \(X_ 1,X_ 2,...,X_ n\) be independent random variables with a fixed, common parent distribution for which the p-th moment \(E| X|^ p\) is defined. Then the maximum order statistic \(X_{(n)}\) grows at a rate that is \(o(n^{1/p})\) in expectation, in probability and a.e. Explicit bounds of this order can be given for \(EX_{(n)}\) in terms of the moments of X. Thus the expectation of the extreme grows slowly with the sample size. This observation is applied to the speed-up realized by parallel computation, and to the performance of scheduling policies.

MSC:
90B35 Deterministic scheduling theory in operations research
68W15 Distributed algorithms
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