Article ID Journal Published Year Pages File Type
5129753 Statistics & Probability Letters 2017 6 Pages PDF
Abstract

In this paper, we establish the following characterization of symmetric absolutely continuous distributions and symmetric discrete distributions. Suppose X1,…,Xn is a random sample from a distribution with pdf/pmf fX(x), and X1:n,…,Xn:n are the corresponding order statistics. Then, Xr:n=d−Xn−r+1:n for some r=1,…,n if and only if fX(x)=fX(−x). Here, =d means that the two random variables have the same distribution. In the discrete case, we assume the support to be finite.

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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