Symmetry of a distribution via symmetry of order statistics

Narayanaswamy Balakrishnan and Alessandro Selvitella

Statistics & Probability Letters, 2017, vol. 129, issue C, 367-372

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.

Keywords: Order statistics; Characterization of distributions; Symmetric distributions (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2017.06.023

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