Extremal Results for the Relative-Entropy Ratio of Collinear Probability Distributions

Tight upper and lower bounds on the ratio of relative entropies of two probability distributions with respect to a common third one were established in the authors’ recent work (in Proc. 2018 IEEE Information Theory Workshop, Guangzhou, China, Nov. 2018), where the three distributions are collinear in the standard (n – 1)-simplex. In this paper, we establish some extremal results regarding these two bounds.