Bivariate Dependence Properties of Order Statistics

Philip J. Boland, Myles Hollander, Kumar Joag-Dev and Subhash Kochar

Journal of Multivariate Analysis, 1996, vol. 56, issue 1, 75-89

Abstract: IfX1, ...,Xnare random variables we denote byX(1)[less-than-or-equals, slant]X(2)[less-than-or-equals, slant]...[less-than-or-equals, slant]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 t|X(i)>s] is an increasing function ofs. This is a stronger form of dependence betweenX(i)andX(j)than that of association, but we also show that among the hierarchy of notions of bivariate dependence this is the strongest possible under these circumstances. It is also shown that in this situation,P[X(j)>t|X(i)>s] is a decreasing function ofi=1, ...,nfor any fixeds

Keywords: order; statistics; associated; random; variables; right; corner; set; increasing; right; tail; increasing; stochastically; increasing; TP2property; positively; quadrant; dependent; reliability; counting; processes; exchangeability; finite; sampling; problem; kout; ofnsystem; (null) (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations: View citations in EconPapers (15)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(96)90005-6
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:56:y:1996:i:1:p:75-89

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().