Generalized Symmetric Divergence Measures and Inequalities

Details Generalized Symmetric Divergence Measures and Inequalities Generalized Symmetric Divergence Measures and Inequalities

2005-01-19

arxiv.org/abs/math/0501301v1

Mathematics

Statistics Theory

This paper is a part of author's chapter to appear in 'Advances in Imaging and Electron Physics', 2005, Elsevier Publication

Scientific paper

There are three classical divergence measures known in the literature on information theory and statistics. These are namely, Jeffryes-Kullback-Leiber \cite{jef} \cite{kul} \textit{J-divergence}. Sibson-Burbea-Rao \cite{sib} \cite{bur1, bur2} \textit{Jensen-Shannon divegernce}and Taneja \cite{tan3} \textit{Arithemtic-Geometric divergence}. These three measures bears an interesting relationship among each other. The divergence measures like \textit{Hellinger discrimination}, \textit{symmetric}$\chi ^2 - $\textit{divergence}, and \textit{triangular discrimination} are also known in the literature. All these measures can be written as particular cases of Csisz\'{a}r's \textit{f-divergence}. Recently, author proved an inequality relating all the six measures. In this paper our aim is to give one parametric generalizations of the above measures and established relationships among them. A new measure similar to \textit{Hellinger's} and \textit{triangular discriminations} is also derived.

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