Converses of the Edmundson-Lah-Ribaric inequality for the generalized Csiszar divergence with applications to Zipf-Mandelbrot law

Abstract

In this paper we obtain some estimates for the generalized f-divergence functional via converses of the Jensen and Edmundson-Lah-Ribaric inequalities for convex functions, and then we obtain some estimates for the Kullback-Leibler divergence. All of the obtained results are applied to Zipf-Mandelbrot law and Zipf law.