Asymptotic theory of extreme dual generalized order statistics

被引:14
作者
Barakat, H. M. [2 ]
El-Adll, Magdy E. [1 ]
机构
[1] Helwan Univ, Fac Sci, Dept Math, Ain Helwan, Egypt
[2] Zagazig Univ, Fac Sci, Dept Math, Zagazig, Egypt
关键词
MAX STABLE LAWS; DISTRIBUTIONS; NORMALIZATION; ATTRACTION; DOMAINS;
D O I
10.1016/j.spl.2009.01.015
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
In a wide subclass of dual generalized order statistics (dgos) (which contains the most important models of descendingly ordered random variables), when the parameters gamma(1), ... , gamma(n) are assumed to be pairwise different, we study the weak convergence of the lower extremes, under general strongly monotone continuous transformations. It is revealed that the weak convergence of the maximum order statistics guarantees the weak convergence of any lower extreme dgos. Moreover, under linear and power normalization and by a suitable choice of these normalizations, the possible weak limits of any rth upper extreme order statistic are the same as the possible weak limits of the rth lower extreme dgos. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码:1252 / 1259
页数:8
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