Inequalities Among Symmetric Divergence Measures and Their Refinement

TL;DR

This paper explores inequalities among six symmetric divergence measures in information theory, providing refined bounds and improving previous inequalities, thus deepening understanding of their relationships.

Contribution

It introduces new inequalities and refinements among symmetric divergence measures, enhancing the theoretical framework of divergence relationships.

Findings

Established new inequalities among divergence measures.

Refined existing inequalities for better bounds.

Improved inequalities previously proposed by Dragomir et al.

Abstract

There are three classical divergence measures in the literature on information theory and statistics, namely, Jeffryes-Kullback-Leiber's J-divergence, Sibson-Burbea-Rao's Jensen-Shannon divegernce and Taneja's arithemtic-geometric mean divergence. These bear an interesting relationship among each other and are based on logarithmic expressions. The divergence measures like Hellinger discrimination, symmetric chi-square divergence, and triangular discrimination are not based on logarithmic expressions. These six divergence measures are symmetric with respect to probability distributions. In this paper some interesting inequalities among these symmetric divergence measures are studied. Refinement over these inequalities is also given. Some inequalities due to Dragomir et al. are also improved.