Bivariate Dependence Properties of Order Statistics
Bivariate Dependence Properties of Order Statistics
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DOI：
10.1006/jmva.1996.0005
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发表时间：
1996
影响因子：
1.6
通讯作者：
P. Boland;M. Hollander;K. Joag-dev;S. Kochar
中科院分区：
文献类型：
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作者：
P. Boland;M. Hollander;K. Joag-dev;S. Kochar
如果X1，？，Xn是随机变量，我们记为X（1）？X（2）？X（n）它们各自的顺序统计量。在随机变量是独立同分布的情况下，人们可以证明任意两个阶矩X（i）和X（j）之间有很强的相关性。如果特别是随机变量与公共密度或质量函数无关，则X（i）和X（j）对于任何i和j都是TP 2依赖的。本文考虑随机变量X1，？，Xn是独立的，但在其他方面是任意分布的。我们证明对于anyi
IfX1, ?,Xnare random variables we denote byX(1)?X(2)???X(n)their respective order statistics. In the case where the random variables are independent and identically distributed, one may demonstrate very strong notions of dependence between any two order statisticsX(i)andX(j). If in particular the random variables are independent with a common density or mass function, thenX(i)andX(j)areTP2dependent for anyiandj. In this paper we consider the situation in which the random variablesX1, ?,Xnare independent but otherwise arbitrarily distributed. We show that for anyi