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May, 1985 Limiting Multivariate Distributions of Intermediate Order Statistics
Bruce Cooil
Ann. Probab. 13(2): 469-477 (May, 1985). DOI: 10.1214/aop/1176993003


Let $Z^{(n)}_m$ represent the $m$th largest order statistic in a random sample of size $n$ from a distribution $F$. If $m = m(n)$ is an intermediate sequence such that $m \rightarrow \infty$ and $m/n \rightarrow 0$ as $n \rightarrow \infty$, the intermediate order statistics of the form $Z^{(n)}_{\lbrack mt_1\rbrack}, \cdots, Z^{(n)}_{\lbrack mt_k\rbrack}$, for $0 < t_1 < \cdots < t_k$, can be used jointly for making statistical inferences about the upper tail of $F$. We find the asymptotic joint distribution of order statistics of this form, for various types of underlying distributions $F$, by determining the limit (weak convergence) of a stochastic process of the form $(Z^{(n)}_{\lbrack mt\rbrack} - \beta^{(n)}_{mt})/\alpha^{(n)}_{mt}, t > 0$, for appropriate normalizing functions $\alpha^{(n)}_{mt}, > 0, \beta^{(n)}_{mt}$.


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Bruce Cooil. "Limiting Multivariate Distributions of Intermediate Order Statistics." Ann. Probab. 13 (2) 469 - 477, May, 1985.


Published: May, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0572.62024
MathSciNet: MR781417
Digital Object Identifier: 10.1214/aop/1176993003

Primary: 60F05
Secondary: 60J65 , 62H05

Keywords: domain of attraction , extremal distribution , Intermediate order statistics , Pareto

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 2 • May, 1985
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