Fisher-like Metrics Associated with ϕ -Deformed (Naudts) Entropies

Cristina-Liliana Pripoae, Iulia-Elena Hirica, Gabriel-Teodor Pripoae () and Vasile Preda
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Cristina-Liliana Pripoae: Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana 6, RO-010374 Bucharest, Romania
Iulia-Elena Hirica: Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania
Gabriel-Teodor Pripoae: Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania
Vasile Preda: Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 22, 1-26

Abstract: The paper defines and studies new semi-Riemannian generalized Fisher metrics and Fisher-like metrics, associated with entropies and divergences. Examples of seven such families are provided, based on exponential PDFs. The particular case when the basic entropy is a ϕ -deformed one, in the sense of Naudts, is investigated in detail, with emphasis on the variation of the emergent scalar curvatures. Moreover, the paper highlights the impact on these geometries determined by the addition of some group logarithms.

Keywords: ? -deformed (Naudts) entropy; divergence; relative group entropy; generalized Fisher metric; Fisher-like metric; MaxEnt problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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