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

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

2005-01-19

arxiv.org/abs/math/0501299v1

Mathematics

Statistics Theory

Scientific paper

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.

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