Generalized non-symmetric divergence measures and inequaities

Abstract

In this paper we consider one parameter generalizations of some non-symmetric divergence measures. Measures are relative information, x²-divergence, relative J -divergence, relative Jensen-Shannon divergence and relative arithmetic and geometric divergence. All the generalizations considered can be written as particular cases of Csiszár f -divergence. By conditioning the probability distributions, relationships among the relative divergence measures are obtained.

Keywords:

• Relative information of type s
• relative J -divergence of type s
• relative JS-divergence of type s
• relative AG-divergence of type s
• Csiszár f -divergence
• information inequalities