Stochastic orderings between distributions and their sample spacings - II

Baha-Eldin Khaledi and Subhash Kochar

Statistics & Probability Letters, 1999, vol. 44, issue 2, 161-166

Abstract: Let X1:n[less-than-or-equals, slant]X2:n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn:n denote the order statistics of a random sample of size n from a probability distribution with distribution function F. Similarly, let Y1:m[less-than-or-equals, slant]Y2:m[less-than-or-equals, slant]...[less-than-or-equals, slant]Ym:m denote the order statistics of an independent random sample of size m from another distribution with distribution function G. We assume that F and G are absolutely continuous with common support (0,[infinity]). The corresponding normalized spacings are defined by Ui:n[reverse not equivalent](n-i+1)(Xi:n-Xi-1:n) and Vj:m[reverse not equivalent](m-j+1)(Yj:m-Yj-1:m), for i=1,...,n and j=1,...,m, where X0:n=Y0:n[reverse not equivalent]0. It is proved that if X is smaller than Y in the hazard rate order sense and if either F or G is a decreasing failure rate (DFR) distribution, then Ui:n is stochastically smaller than Vj:m for i[less-than-or-equals, slant]j and n-i[greater-or-equal, slanted]m-j. If instead, we assume that X is smaller than Y in the likelihood ratio order and if either F or G is DFR, then this result can be strengthened from stochastic ordering to hazard rate ordering. Finally, under a stronger assumption on the shapes of the distributions that either F or G has log-convex density, it is proved that X being smaller than Y in the likelihood ratio order implies that Ui:n is smaller than Vj:m in the sense of likelihood ratio ordering for i[less-than-or-equals, slant]j and n-i=m-j.

Keywords: Likelihood; ratio; ordering; Hazard; rate; ordering; Stochastic; ordering; Dispersive; ordering; Normalized; spacings (search for similar items in EconPapers)
Date: 1999
References: View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(99)00004-8
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:stapro:v:44:y:1999:i:2:p:161-166

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

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().