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Zipf-Mandelbrot law and superadditivity of the Jensen functional

Superadditivity property of the discrete Jensen functional is brought in relation to the Csiszar divergence functional. Its monotonicity property and specific bounds are observed consequently in the same context. Some of the well known f− divergences, e.g. the Kullback-Leibler divergence, the Hellinger distance, the Bhattacharyya coefficient, the chi-square divergence and the total variation distance are analyzed in a similar way. All obtained inequalities are eventually interpreted in the environment of the Zipf and the Zipf-Mandelbrot law.

Jensen functional, superadditivity, Zipf and Zipf-Mandelbrot law, Csiszar divergences

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