Equivalent characterizations on orderings of order statistics and sample ranges

  • Authors:

  • Tiantian Mao;Taizhong Hu

  • Affiliations:

  • Department of statistics and finance, university of science and technology of china, hefei, anhui 230026, people's republic of china e-mail: mttiy@mail.ustc.edu.cn/ thu@ustc.edu.cn;Department of statistics and finance, university of science and technology of china, hefei, anhui 230026, people's republic of china e-mail: mttiy@mail.ustc.edu.cn/ thu@ustc.edu.cn

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2010

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Abstract

The purpose of this article is to present several equivalent characterizations of comparing the largest-order statistics and sample ranges of two sets of n independent exponential random variables with respect to different stochastic orders, where the random variables in one set are heterogeneous and the random variables in the other set are identically distributed. The main results complement and extend several known results in the literature. The geometric distribution can be regarded as the discrete counterpart of the exponential distribution. We also study the orderings of the largest-order statistics from geometric random variables and point out similarities and differences between orderings of the largest-order statistics from geometric variables and from exponential variables.