Distribution-free bounds on the expectation of the maximum with scheduling applications

  • Authors:

  • Peter J. Downey

  • Affiliations:

  • Department of Computer Science, The University of Arizona, Tucson AZ 85721, USA

  • Venue:
  • Operations Research Letters
  • Year:
  • 1990

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Abstract

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 statistics 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.