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July, 1986 The Asymptotic Distribution of Sums of Extreme Values from a Regularly Varying Distribution
Sandor Csorgo, David M. Mason
Ann. Probab. 14(3): 974-983 (July, 1986). DOI: 10.1214/aop/1176992451

Abstract

Let $X_{1,n} \leqq \cdots \leqq X_{n,n}$ be the order statistics of $n$ independent and identically distributed positive random variables with common distribution function $F$ satisfying $1 - F(x) = x^{-\alpha}L^\ast(x), x > 0$, where $\alpha$ is any positive number and $L^\ast$ is any function slowly varying at infinity. We give a complete description of the asymptotic distribution of the sum of the top $k_n$ extreme values $X_{n+1-k_n,n}, X_{n+2-k_n,n}, \ldots, X_{n,n}$ for any sequence of positive integers $k_n$ such that $k_n \rightarrow \infty$ and $k_n/n \rightarrow 0$ as $n \rightarrow \infty$.

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Sandor Csorgo. David M. Mason. "The Asymptotic Distribution of Sums of Extreme Values from a Regularly Varying Distribution." Ann. Probab. 14 (3) 974 - 983, July, 1986. https://doi.org/10.1214/aop/1176992451

Information

Published: July, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0593.60034
MathSciNet: MR841597
Digital Object Identifier: 10.1214/aop/1176992451

Subjects:
Primary: 60F05
Secondary: 62G30

Keywords: asymptotic distribution , regular variation , sums of extreme values

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 3 • July, 1986
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