Global properties of the symmetrized $s$-divergence

TL;DR

This paper investigates the properties of symmetrized s-divergences, establishing fundamental characteristics like symmetry, monotonicity, and log-convexity, and proves a key convexity result relevant to divergence measures.

Contribution

It introduces and analyzes the symmetrized s-divergences, providing new theoretical insights into their mathematical properties and convexity behavior.

Findings

Symmetry, monotonicity, and log-convexity of the symmetrized divergences are established.

A significant convexity property of the divergences is proved.

The study enhances understanding of divergence measures in information theory.

Abstract

In this paper we give a study of the symmetrized divergences $U_s(p,q)=K_s(p||q)+K_s(q||p)$ and $V_s(p,q)=K_s(p||q)K_s(q||p)$, where $K_s$ is the relative divergence of type $s, s\in\mathbb R$. Some basic properties as symmetry, monotonicity and log-convexity are established. An important result from the Convexity Theory is also proved.