Bivariate Dependence Properties of Order Statistics
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
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 56 (1996)
Issue (Month): 1 (January)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:56:y:1996:i:1:p:75-89. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.