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ϕ-Informational Measures: Some Results and Interrelations

Abstract : In this paper, we focus on extended informational measures based on a convex function ϕ: entropies, extended Fisher information, and generalized moments. Both the generalization of the Fisher information and the moments rely on the definition of an escort distribution linked to the (entropic) functional ϕ. We revisit the usual maximum entropy principle—more precisely its inverse problem, starting from the distribution and constraints, which leads to the introduction of state-dependent ϕ-entropies. Then, we examine interrelations between the extended informational measures and generalize relationships such the Cramér–Rao inequality and the de Bruijn identity in this broader context. In this particular framework, the maximum entropy distributions play a central role. Of course, all the results derived in the paper include the usual ones as special cases.
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https://hal.archives-ouvertes.fr/hal-03294418
Contributor : Steeve Zozor Connect in order to contact the contributor
Submitted on : Wednesday, July 21, 2021 - 3:41:18 PM
Last modification on : Friday, April 1, 2022 - 3:44:59 AM

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Steeve Zozor, Jean-François Bercher. ϕ-Informational Measures: Some Results and Interrelations. Entropy, MDPI, 2021, 23 (7), pp.911. ⟨10.3390/e23070911⟩. ⟨hal-03294418⟩

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