Inequalities for Information Potentials and Entropies

Ana Maria Acu, Alexandra Măduţa, Diana Otrocol and Ioan Raşa
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Ana Maria Acu: Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5-7, RO-550012 Sibiu, Romania
Alexandra Măduţa: Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
Diana Otrocol: Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
Ioan Raşa: Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania

Mathematics, 2020, vol. 8, issue 11, 1-18

Abstract: We consider a probability distribution p 0 ( x ) , p 1 ( x ) , … depending on a real parameter x . The associated information potential is S ( x ) : = ∑ k p k 2 ( x ) . The Rényi entropy and the Tsallis entropy of order 2 can be expressed as R ( x ) = − log S ( x ) and T ( x ) = 1 − S ( x ) . We establish recurrence relations, inequalities and bounds for S ( x ) , which lead immediately to similar relations, inequalities and bounds for the two entropies. We show that some sequences R n ( x ) n ≥ 0 and T n ( x ) n ≥ 0 , associated with sequences of classical positive linear operators, are concave and increasing. Two conjectures are formulated involving the information potentials associated with the Durrmeyer density of probability, respectively the Bleimann–Butzer–Hahn probability distribution.

Keywords: probability distribution; Rényi entropy; Tsallis entropy; information potential; functional equations; inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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