On the Convexity of Some Divergence Measures Based on Entropy Functions

摘要

Three measures of divergence between vectors in a convex set of an n-dimensional real vector space have been defined in terms of certain types of entropy functions, and their convexity property studied. Among other results, a classification of the alpha-order entropies is obtained by the convexity of these measures. These results have applications to the measurement of diversity of a discrete probability distribution and divergence between two distributions. (Author)