Some inequalities relating different measures of divergence between two probability distributions

Abstract

This note presents new inequalities relating different divergence measures in the family of "convex likelihood-ratio expectation" measures of Csiszar (1967), Ali and Silvey (1966), and especially in the single-parameter family of "AM-GM" divergence measures. The most prominent result is that /spl theta//sup 2//spl les/ 1/4 J, where /spl theta/ is the Bhattacharyya angle of divergence (a true distance metric), and J is the symmetric cross-entropy. A pair of "log /spl Gamma/" divergences is also introduced and related to the cross-entropies I and J.