Abstract/Details

Stochastic orders and dependence properties of concomitants of order statistics


1999 1999

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Abstract (summary)

Given a bivariate sample [special characters omitted], the rth order statistic [special characters omitted] is the rth smallest value of the X's and the rth concomitant [special characters omitted] is the Y value that accompanies [special characters omitted]. Order statistics are widely used, and their stochastic order and dependence properties have been studied extensively. In this dissertation, we show that if X and Y are positively dependent, then the concomitants satisfy certain stochastic order relations and positive dependence properties as well, at least in the case where the vectors ( Xi, Yi) are independent and identically distributed and come from an absolutely continuous distribution.

It, is shown that if Y is stochastically increasing in X, the concomitants increase in multivariate stochastic order, and the entire vector of concomitants [special characters omitted] is multivariate associated. If the conditional hazard rate function of Y given X, [special characters omitted] is decreasing in x, [special characters omitted] is multivariate right corner set increasing. If X and Y are totally positive dependent of order 2, then [special characters omitted] is multivariate totally positive dependent of order 2, and the univariate concomitants [special characters omitted] increase in likelihood ratio order as r increases.

Concomitants have not previously been studied in the discrete case much because, unlike the continuous case, the probability that two order statistics [special characters omitted] and [special characters omitted] are equal is positive; thus, the concomitants are not immediately determinable. Here we introduce a way of assigning concomitants in the discrete case and prove two related results for that case.

Indexing (details)


Subject
Statistics;
Mathematics
Classification
0463: Statistics
0405: Mathematics
Identifier / keyword
Pure sciences; Concomitants; Dependence; Order statistics; Stochastic orders
Title
Stochastic orders and dependence properties of concomitants of order statistics
Author
Blessinger, Todd David
Number of pages
78
Publication year
1999
Degree date
1999
School code
0118
Source
DAI-B 60/05, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780599328693, 059932869X
Advisor
Korwar, Ramesh
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9932295
ProQuest document ID
304515068
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304515068
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