Refinement Inequalities among Symmetric Divergence Measures

There are three classical divergence measures in the literature on information theory and statistics, namely, Jeffryes-Kullback-Leiber’s J-divergence, Sibson-Burbea-Rao’s JensenShannon divegernce and Taneja’s arithemtic geometric mean divergence. These bear an interesting relationship among each other and are based on logarithmic expressions. The divergence measures like Hellinger discrimination, symmetric χ−divergence, and triangular discrimination are not based on logarithmic expressions. These six divergence measures are symmetric with respect to probability distributions. In this paper some interesting inequalities among these symmetric divergence measures are studied. Refinements of these inequalities are also given. Some inequalities due to Dragomir et al. [6] are also improved.