Orderings arising from expected extremes, with an application. (English) Zbl 1400.60074

Downey, Peter J.; Maier, Robert S.

Shaked, Moshe (ed.) et al., Stochastic inequalities. Collection of papers of conference, one of the 1991 AMS-IMS-SIAM joint summer research conferences, Seattle, WA, USA, July 1991. Hayward, CA: IMS, Institute of Mathematical Statistics (ISBN 0-940600-29-3). IMS Lect. Notes, Monogr. Ser. 22, 66-75 (1992).

Summary: We bound the expected maximum order statistics \(\{EX_{(n)}\}^{\infty}_{n=1}\) of a d.f. \(F_X\) both above and below. Our results have an interpretation in terms of stochastic orderings \(\leq _e\) and \(\leq_{we}\) defined as follows: \(F_X \leq_e F_Y\) iff \(EX_{(n)} \leq EY_{(n)}\) for all \(n\), and \(F_X \leq_{we} F_Y\) iff \(EX_{(n)} \leq EY_{(n)}\) for \(n\) sufficiently large. We apply our results on \(\leq_{we}\) to the end-to-end delay in a resequencing \(\mathrm{M}/\mathrm{G}/\infty\) queue
For the entire collection see [Zbl 0920.00039].

MSC:

60G70	Extreme value theory; extremal stochastic processes
60E05	Probability distributions: general theory
60K25	Queueing theory (aspects of probability theory)

Keywords:

extreme order statistics; stochastic orderings; stochastic inequalities; resequencing delay; heavy traffic limit