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

Mirna Rodić
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Mirna Rodić: Faculty of Textile Technology, University of Zagreb, 10000 Zagreb, Croatia

Mathematics, 2022, vol. 10, issue 6, 1-14

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.

Keywords: Green function; converse Jensen inequality; f-divergence; Zipf–Mandelbrot law (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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