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

共 50 条

[21] UNIFORM APPROXIMATION TO DISTRIBUTIONS OF EXTREME ORDER-STATISTICS
REISS, RD
ADVANCES IN APPLIED PROBABILITY, 1981, 13 (03) : 533 - 547
[22] A note on domains of attraction of the limit laws of intermediate order statistics under power normalization
Barakat, H. M.
Omar, A. R.
STATISTICAL METHODOLOGY, 2016, 31 : 1 - 7
[23] Extreme value modeling under power normalization
Barakat, H. M.
Nigm, E. M.
Khaled, O. M.
APPLIED MATHEMATICAL MODELLING, 2013, 37 (24) : 10162 - 10169
[24] RANDOM-WALK AND DISTRIBUTIONS OF RANK ORDER STATISTICS
ANEJA, KG
SEN, K
SIAM JOURNAL ON APPLIED MATHEMATICS, 1972, 23 (02) : 276 - &
[25] Comparison of extreme order statistics from two sets of heterogeneous dependent random variables under random shocks
Amini-Seresht, Ebrahim
Nasiroleslami, Ebrahim
Balakrishnan, Narayanaswamy
METRIKA, 2024, 87 (02) : 133 - 153
[26] Comparison of extreme order statistics from two sets of heterogeneous dependent random variables under random shocks
Ebrahim Amini-Seresht
Ebrahim Nasiroleslami
Narayanaswamy Balakrishnan
Metrika, 2024, 87 : 133 - 153
[27] On extreme order statistics from heterogeneous beta distributions with applications
Zhao, Peng
Wang, Lei
Zhang, Yiying
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2017, 46 (14) : 7020 - 7038
[28] LIMIT DISTRIBUTIONS FOR COMPOUNDED SUMS OF EXTREME ORDER-STATISTICS
BEIRLANT, J
TEUGELS, JL
JOURNAL OF APPLIED PROBABILITY, 1992, 29 (03) : 557 - 574
[29] A NOTE ON UNIFORM APPROXIMATION TO DISTRIBUTIONS OF EXTREME ORDER-STATISTICS
KOHNE, W
REISS, RD
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1983, 35 (03) : 343 - 345
[30] Domains of attraction of asymptotic distributions of extreme generalized order statistics
Schmiedt, Anja B.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2016, 45 (07) : 2089 - 2104

← 1 2 3 4 5 →