Conditional ordering of order statistics

  • Authors:

  • Weiwei Zhuang;Junchao Yao;Taizhong Hu

  • Affiliations:

  • Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China;Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China;Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2010

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Abstract

For any positive integers m and n, let X"1,X"2,...,X"m"@?"n be independent random variables with possibly nonidentical distributions. Let X"1":"n@?X"2":"n@?...@?X"n":"n be order statistics of random variables X"1,X"2,...,X"n, and let X"1":"m@?X"2":"m@?...@?X"m":"m be order statistics of random variables X"1,X"2,...,X"m. It is shown that (X"j":"n,X"j"+"1":"n,...,X"n":"n) given X"i":"my for j-i=max{n-m,0}, and (X"1":"n,X"2":"n,...,X"j":"n) given X"i":"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 Haggstrom (2008) [1] and Hu and Chen (2008) [2].