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Stochastic comparisons of order statistics and their concomitants

Author

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  • Bairamov, Ismihan
  • Khaledi, Baha-Eldin
  • Shaked, Moshe

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.

Suggested Citation

  • Bairamov, Ismihan & Khaledi, Baha-Eldin & Shaked, Moshe, 2014. "Stochastic comparisons of order statistics and their concomitants," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 105-115.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:105-115
    DOI: 10.1016/j.jmva.2013.10.013
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    References listed on IDEAS

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    1. Bairamov, I. & Stepanov, A., 2011. "Numbers of near bivariate record-concomitant observations," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 908-917, May.
    2. Wang, Ke & Nagaraja, H.N., 2009. "Concomitants of order statistics for dependent samples," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 553-558, February.
    3. Belzunce, Félix & Mercader, José-Angel & Ruiz, José-María & Spizzichino, Fabio, 2009. "Stochastic comparisons of multivariate mixture models," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1657-1669, September.
    4. Blessinger, Todd, 2002. "More on Stochastic Comparisons and Dependence among Concomitants of Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 367-378, August.
    5. Li, Haijun & Scarsini, Marco & Shaked, Moshe, 1996. "Linkages: A Tool for the Construction of Multivariate Distributions with Given Nonoverlapping Multivariate Marginals," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 20-41, January.
    6. Khaledi, Baha-Eldin & Kochar, Subhash, 2000. "Stochastic Comparisons and Dependence among Concomitants of Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 262-281, May.
    7. Bairamov, Ismihan, 2012. "Majorization bounds for distribution functions," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1799-1806.
    8. Joag-dev, Kumar & Kochar, Subhash & Proschan, Frank, 1995. "A general composition theorem and its applications to certain partial orderings of distributions," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 111-119, February.
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