Some Information Properties of Order Statistics of Skew-normal Distribution

Accepted - June 2023

Abstract

The skew-normal distribution and some of its extensions have been considered in the last two decades in view of distribution theory and the associated properties. However, less attention has been paid to other aspects of this family of distributions. In this paper, we focus on the information properties of this distribution and the distributions of order statistics of a simple random sample from the skew-normal distribution. The Shannon’s entropy as well as Kullback-Leibler divergence between the order statistics of two independent skew-normal distributions are studied. Some interesting properties of the information measures of different order statistics are presented.