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On the Converse Jensen-Type Inequality for Generalized f -Divergences and Zipf–Mandelbrot Law

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  • Mirna Rodić

    (Faculty of Textile Technology, University of Zagreb, 10000 Zagreb, Croatia)

Abstract

Motivated by some recent investigations about the sharpness of the Jensen inequality, this paper deals with the sharpness of the converse of the Jensen inequality. These results are then used for deriving new inequalities for different types of generalized f -divergences. As divergences measure the differences between probability distributions, these new inequalities are then applied on the Zipf–Mandelbrot law as a special kind of a probability distribution.

Suggested Citation

  • Mirna Rodić, 2022. "On the Converse Jensen-Type Inequality for Generalized f -Divergences and Zipf–Mandelbrot Law," Mathematics, MDPI, vol. 10(6), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:947-:d:772331
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