# zbMATH — the first resource for mathematics

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