Limiting distributions of extreme order statistics under power normalization and random index

被引：9

作者：

Peng, Zuoxiang ^{[2
]}

Jiang, Qin ^{[2
]}

Nadarajah, Saralees ^{[1
]}

机构：

[1] Univ Manchester, Sch Math, Manchester, Lancs, England

[2] Southwest Univ, Sch Math & Stat, Chongqing, Peoples R China

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2012年 / 84卷 / 04期

关键词：

limiting distribution; order statistic; power normalization; random index; shifted distribution; MAX DOMAINS; ATTRACTION; UNIVARIATE;

D O I：

10.1080/17442508.2011.573072

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (X-n) be a sequence of independent and identically distributed random variables and let M-n((s)) denote the sth largest order statistic of X-k, 1 <= k <= n. In this note, the limiting distributions of M-Nn((s)) under power normalization are derived as the integer-valued random index N-n follows the shifted negative binomial, shifted Poisson and shifted binomial distributions.

引用

页码：553 / 560

页数：8

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