Conditional ordering of order statistics |
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Authors: | Weiwei Zhuang |
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Institution: | Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China |
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Abstract: | For any positive integers m and n, let X1,X2,…,Xm∨n be independent random variables with possibly nonidentical distributions. Let X1:n≤X2:n≤?≤Xn:n be order statistics of random variables X1,X2,…,Xn, and let X1:m≤X2:m≤?≤Xm:m be order statistics of random variables X1,X2,…,Xm. It is shown that (Xj:n,Xj+1:n,…,Xn:n) given Xi:m>y for j−i≥max{n−m,0}, and (X1:n,X2:n,…,Xj:n) given Xi:m≤y for j−i≤min{n−m,0} are all increasing in y with respect to the usual multivariate stochastic order. We thus extend the main results in Dubhashi and Häggström (2008) 1] and Hu and Chen (2008) 2]. |
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Keywords: | 60E15 60K10 |
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