On the symmetrized s-divergence

Abstract

In this study, we work with the relative divergence of type s,s∈ℝs,s\in {\mathbb{R}}, which includes the Kullback-Leibler divergence and the Hellinger and χ 2 distances as particular cases. We study the symmetrized divergences in additive and multiplicative forms. Some basic properties such as symmetry, monotonicity and log-convexity are established. An important result from the convexity theory is also proved.

Keywords

• relative divergence of type s
• monotonicity
• log-convexity
• 60e15