A Sequence of Inequalities among Difference of Symmetric Divergence Measures

TL;DR

This paper establishes a sequence of inequalities among various symmetric divergence measures, including both logarithmic and non-logarithmic types, through the analysis of two parametric generalizations.

Contribution

It introduces two parametric generalizations of divergence measures and derives a sequence of inequalities connecting well-known divergence measures.

Findings

Established inequalities among divergence measures.

Unified various divergence measures under a common framework.

Provided new bounds and relationships among divergence measures.

Abstract

In this paper we have considered two one parametric generalizations. These two generalizations have in articular the well known measures such as: J-divergence, Jensen-Shannon divergence and Arithmetic-Geometric mean divergence. These three measures are with logarithmic expressions. Also, we have particular cases the measures such as: Hellinger discrimination, symmetric chi-square divergence, and triangular discrimination. These three measures are also well-known in the literature of statistics, and are without logarithmic expressions. Still, we have one more non logarithmic measure as particular case calling it d-divergence. These seven measures bear an interesting inequality. Based on this inequality, we have considered different difference of divergence measures and established a sequence of inequalities among themselves.