engleski

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

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.

discrete Jensen’s inequality ; f-divergence ; Rényi divergence ; entropy

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