[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5351/CKSS.2006.13.2.243

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)

Publication Information

Communications for Statistical Applications and Methods / v.13, no.2, 2006 , pp. 243-254 More about this Journal

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 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.

Keywords

Order statistic; Probability mass function; Probability density function; Relative frequency;

Citations & Related Records

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