Relative Divergence Measures and Information Inequalities

There are many information and divergence measures exist in the literature on information theory and statistics. The most famous among them are Kullback-Leiber’s [17] relative information and Jeffreys [16] J-divergence, Information radius or Jensen difference divergence measure due to Sibson [23]. Burbea and Rao [3, 4] has also found its applications in the literature. Taneja [25] studied another kind of divergence measure based on arithmetic and geometric means. These three divergence measures bear a good relationship among each other. But there are another measures arising due to J-divergence, JS-divergence and AG-divergence. These measures we call here relative divergence measures or non-symmetric divergence measures. Here our aim is to obtain bounds on symmetric and non-symmetric divergence measures in terms of relative information of type s using properties of Csiszár’s f-divergence.