ϕ-Informational Measures: Some Results and Interrelations

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) functi...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2021-07, Vol.23 (7), p.911
Main Authors: Zozor, Steeve, Bercher, Jean-François
Format: Article
Language:English
Subjects:
(inverse) maximum ϕ-entropy problem
Communication
Computer Science
Entropy
Equilibrium
Fisher information
Inequality
Information Theory
Inverse problems
Maximum entropy
Mean square errors
Physics
Probability distribution
Random variables
state-dependent ϕ-entropy
ϕ-entropy
ϕ-escort distributions
ϕ-Fisher information
ϕ-moments
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Summary: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.
ISSN:1099-4300
1099-4300
DOI:10.3390/e23070911