Global properties of the symmetrized $s$-divergence

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.