 Stochastic comparisons of order statistics and their concomitantsIsmihan Bairamov, Baha-Eldin Khaledi and Moshe Shaked Journal of Multivariate Analysis, 2014, vol. 124, issue C, 105-115 Abstract: Let X1:n≤X2:n⋯≤Xn:n be the order statistics from some sample, and let Y[1:n],Y[2:n],…,Y[n:n] be the corresponding concomitants. One purpose of this paper is to obtain results that stochastically compare, in various senses, the random vector (Xr:n,Y[r:n]) to the random vector (Xr+1:n,Y[r+1:n]), r=1,2,…,n−1. Such comparisons are called one-sample comparisons. Next, let S1:n≤S2:n⋯≤Sn:n be the order statistics constructed from another sample, and let T[1:n],T[2:n],…,T[n:n] be the corresponding concomitants. Another purpose of this paper is to obtain results that stochastically compare, in various senses, the random vector (Xr:n,Y[r:n]) with the random vector (Sr:n,T[r:n]), r=1,2,…,n. Such comparisons are called two-sample comparisons. It is shown that some of the results in this paper strengthen previous results in the literature. Some applications in reliability theory are described. Keywords: Positive quadrant dependence (PQD); Multivariate ordinary stochastic order; Multivariate hazard rate order; Multivariate likelihood ratio order; Stochastic monotonicity; r-out-of-n systems; Total positivity (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:124:y:2014:i:c:p:105-115 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2013.10.013 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 |
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