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

In this paper we obtain some estimates for the generalized f-divergence functional via converses of the Jensen and Edmundson-Lah-Ribarič 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. © 2018 Sobolev Institute of Mathematics.