On Cumulative Tsallis Entropies

Simon, Thomas; Dulac, Guillaume

Type de document :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1007/s10440-023-00620-3

Titre :

On Cumulative Tsallis Entropies

Auteur(s) :

Simon, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Dulac, Guillaume [Auteur]

Titre de la revue :

Acta Applicandae Mathematicae

Pagination :

Éditeur :

Springer Verlag

Date de publication :

2023-11-13

ISSN :

0167-8019

Discipline(s) HAL :

Mathématiques [math]
Statistiques [stat]

Résumé en anglais : [en]

We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs ...
Lire la suite >We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs statistics. This functional is here considered as a perturbation of the expected mean residual life via some power weight function. This point of view leads to the introduction of the dual cumulative Tsallis entropy and of two families of coherent risk measures generalizing those built on mean residual life. We characterize the finiteness of the cumulative Tsallis entropy in terms of Lp-spaces and show how they determine the underlying distribution. The range of the functional is exactly described under various constraints, with optimal bounds improving on all those previously available in the literature. Whereas the maximization of the Tsallis differential entropy gives rise to the classical q-Gaussian distribution which is a generalization of the Gaussian having a finite range or heavy tails, the maximization of the cumulative Tsallis entropy leads to an analogous perturbation of the Logistic distribution.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Fichiers

2210.09047
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