Estimations of f- and Rényi divergences by using a cyclic refinement of the Jensen's inequality

Horváth, László and Pečarić, Gilda and Pečarić, Josip (2019) Estimations of f- and Rényi divergences by using a cyclic refinement of the Jensen's inequality. BULLETIN OF MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 42 (3). pp. 933-946. ISSN 0126-6705

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Abstract

The Jensen's inequality plays a crucial role to obtain inequalities for divergences between probability distributions. In this paper we introduce a new functional, based on the f-divergence functional, and then we obtain some estimates for the new functional, the f-divergence and the Rényi divergence by applying a cyclic refinement of the Jensen's inequality. Some inequalities for Rényi and Shannon entropies are obtained too. Zipf-Mandelbrot law is used to illustrate the results.

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