Generalization of F-Divergence Measures for Probability Distributions with Associated Utilities

Abstract

In this paper, f-divergence measures have been generalized for probability distributions with associated utility distribution. The defined generalized ‘useful’ divergence measures have been introduced and studied for convex functions. The defined new generalized ‘useful’ Rényi type f?divergences like ‘useful’ Jensen?Rényi and ‘useful’ Jeffreys?Rényi approach the generalized Rényi type f?divergences when the utilities are ignored. Few inequalities relating to non-negative convex functions have also been introduced for defined new generalized ‘useful’ Rényi type f?divergences. Some examples of acknowledged divergence measures have been familiarized in order to demonstrate some utilities of new divergence measures.