On Unified Generalizations of Relative Jensen--Shannon and Arithmetic--Geometric Divergence Measures, and Their Properties

TL;DR

This paper introduces a parametric generalization of various non-symmetric divergence measures, unifying them under the f-divergence framework and deriving bounds under certain conditions.

Contribution

It proposes a unified parametric generalization of divergence measures and establishes bounds for these measures within the f-divergence framework.

Findings

Unified framework for divergence measures

Derived bounds for generalized divergence measures

Connections among various divergence measures

Abstract

In this paper we shall consider one parametric generalization of some non-symmetric divergence measures. The \textit{non-symmetric divergence measures} are such as: Kullback-Leibler \textit{relative information}, $\chi ^2-$\textit{divergence}, \textit{relative J -- divergence}, \textit{relative Jensen -- Shannon divergence} and \textit{relative Arithmetic -- Geometric divergence}. All the generalizations considered can be written as particular cases of Csisz\'{a}r's \textit{f-divergence}. By putting some conditions on the probability distribution, the aim here is to develop bounds on these measures and their parametric generalizations.