Generalized Non-Symmetric Divergence Measures and Inequalities

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 Csiszár \textit{f-divergence}. By conditioning the probability distributions, relationships among the \textit{relative divergence measures}are obtained.