Relative Frequency of Order Statistics in Independent and Identically Distributed Random Vectors

Title & Authors
Relative Frequency of Order Statistics in Independent and Identically Distributed Random Vectors
Park, So-Ryoung; Kwon, Hyoung-Moon; Kim, Sun-Yong; Song, Iick-Ho;

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 $\small{Pr\{X_{[s]}=x\}}$ is no less than the probability $\small{Pr\{X_{[r]}=x\}}$ at any point $\small{x{\geqq}x_0}$ when r denotes the r-th order statistic of an i.i.d. discrete random vector and $\small{x_0}$ 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;
Language
Korean
Cited by
1.
On the sums of probability functions of order statistics,;;;;;

Journal of the Korean Statistical Society, 2013. vol.42. 2, pp.257-265
1.
On the sums of probability functions of order statistics, Journal of the Korean Statistical Society, 2013, 42, 2, 257
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