Generalized Non-Symmetric Divergence Measures and Inequalities

TL;DR

This paper introduces one-parameter generalizations of various non-symmetric divergence measures, unifying them under Csiszár f-divergence, and explores their relationships through conditioned probability distributions.

Contribution

It presents a unified framework for generalized divergence measures and derives relationships among them using conditional probability distributions.

Findings

Generalizations encompass known divergence measures as special cases.

Relationships among divergence measures are established.

Framework aids in understanding divergence measure properties.

Abstract

In this paper we consider one parameter generalizations of some non - symmetric divergence measures. Measures are \textit{relative information}, $\chi ^2 - $\textit{divergence}, \textit{relative J-divergence}, \textit{relative Jensen-Shannon divergence}and \textit{relative arithmetic and geometric divergence}. All the generalizations considered can be written as particular cases of Csisz\'{a}r \textit{f-divergence}. By conditioning the probability distributions, relationships among the \textit{relative divergence measures}are obtained.