Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5129753 | Statistics & Probability Letters | 2017 | 6 Pages |
Abstract
In this paper, we establish the following characterization of symmetric absolutely continuous distributions and symmetric discrete distributions. Suppose X1,â¦,Xn is a random sample from a distribution with pdf/pmf fX(x), and X1:n,â¦,Xn:n are the corresponding order statistics. Then, Xr:n=dâXnâr+1:n for some r=1,â¦,n if and only if fX(x)=fX(âx). Here, =d means that the two random variables have the same distribution. In the discrete case, we assume the support to be finite.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Narayanaswamy Balakrishnan, Alessandro Selvitella,