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October, 1981 Limit Theorems on Order Statistics
Jozef L. Teugels
Ann. Probab. 9(5): 868-880 (October, 1981). DOI: 10.1214/aop/1176994314

Abstract

Let $F$ belong to the domain of attraction of a stable law with parameters $\alpha$ and $p$. Let $X_1, X_2, \cdots$ be a sample from $F$. Put $|\tilde X_1| \leq |\tilde X_2| \leq \cdots \leq |\tilde X_n|$. We consider the asymptotic properties as $n \rightarrow \infty$ (and $k \rightarrow \infty$) of the ratio of order statistics $(\tilde X_1 + \cdots + \tilde X_{n - k})/|\tilde X_{n - k + 1}|$.

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Jozef L. Teugels. "Limit Theorems on Order Statistics." Ann. Probab. 9 (5) 868 - 880, October, 1981. https://doi.org/10.1214/aop/1176994314

Information

Published: October, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0467.62046
MathSciNet: MR628879
Digital Object Identifier: 10.1214/aop/1176994314

Subjects:
Primary: 62G30
Secondary: 60F05

Keywords: extremal laws , limit theorems , order statistics , regular variation , Stable laws

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 5 • October, 1981
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