Translator Disclaimer
November, 1984 Comparison of Threshold Stop Rules and Maximum for Independent Nonnegative Random Variables
Ester Samuel-Cahn
Ann. Probab. 12(4): 1213-1216 (November, 1984). DOI: 10.1214/aop/1176993150

Abstract

Let $X_i \geq 0$ be independent, $i = 1, \cdots, n$, and $X^\ast_n = \max(X_1, \cdots, X_n)$. Let $t(c) (s(c))$ be the threshold stopping rule for $X_1, \cdots, X_n$, defined by $t(c) = \text{smallest} i$ for which $X_i \geq c(s(c) = \text{smallest} i$ for which $X_i > c), = n$ otherwise. Let $m$ be a median of the distribution of $X^\ast_n$. It is shown that for every $n$ and $\underline{X}$ either $EX^\ast_n \leq 2EX_{t(m)}$ or $EX^\ast_n \leq 2EX_{s(m)}$. This improves previously known results, [1], [4]. Some results for i.i.d. $X_i$ are also included.

Citation

Download Citation

Ester Samuel-Cahn. "Comparison of Threshold Stop Rules and Maximum for Independent Nonnegative Random Variables." Ann. Probab. 12 (4) 1213 - 1216, November, 1984. https://doi.org/10.1214/aop/1176993150

Information

Published: November, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0549.60036
MathSciNet: MR757778
Digital Object Identifier: 10.1214/aop/1176993150

Subjects:
Primary: 60G40

Rights: Copyright © 1984 Institute of Mathematical Statistics

JOURNAL ARTICLE
4 PAGES


SHARE
Vol.12 • No. 4 • November, 1984
Back to Top