Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Relative Frequency of Order Statistics in Independent and Identically Distributed Random Vectors

  • Park, So-Ryoung (School of Information, Communications, and Electronics Engineering, The Catholic University of Korea) ;
  • Kwon, Hyoung-Moon (Department of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST)) ;
  • Kim, Sun-Yong (Department of Electronics Engineering, Konkuk University) ;
  • Song, Iick-Ho (Department of Electrical Engineering, KAIST)
  • Published : 2006.08.31
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Abstract

The relative frequency of order statistics is investigated for independent and identically distributed (i.i.d.) random variables. Specifically, it is shown that the probability $Pr\{X_{[s]}=x\}$ is no less than the probability $Pr\{X_{[r]}=x\}$ at any point $x{\geqq}x_0$ when r$X_{[r]}$ denotes the r-th order statistic of an i.i.d. discrete random vector and $x_0$ depends on the population probability distribution. A similar result for i.i.d. continuous random vectors is also presented.

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