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April, 1979 Stochastic Compactness of Sample Extremes
Laurens de Haan, Geert Ridder
Ann. Probab. 7(2): 290-303 (April, 1979). DOI: 10.1214/aop/1176995089

Abstract

Let $Y_1, Y_2, \cdots$ be independent and identically distributed random variables with common distribution function $F$ and let $X_n = \max\{Y_1, \cdots, Y_n\}$ for $n = 1, 2, \cdots$. Necessary and sufficient conditions (in terms of $F$) are derived for the existence of a sequence of positive constants $\{a_n\}$ such that the sequence $\{X_n/a_n\}$ is stochastically compact. Moreover, the relation between the stochastic compactness of partial maxima and partial sums of the $Y_n$'s is investigated.

Citation

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Laurens de Haan. Geert Ridder. "Stochastic Compactness of Sample Extremes." Ann. Probab. 7 (2) 290 - 303, April, 1979. https://doi.org/10.1214/aop/1176995089

Information

Published: April, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0395.60029
MathSciNet: MR525055
Digital Object Identifier: 10.1214/aop/1176995089

Subjects:
Primary: 60F05
Secondary: 62G30

Keywords: regular variation , sample extremes , stochastic compactness

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 2 • April, 1979
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