On the Entropy and the Maximum Entropy Principle of Uncertain Variables

A new variance formula is developed using the generalized inverse of an increasing function. Based on the variance formula, a new entropy formula for any uncertain variable is provided. Most of the entropy formulas in the literature are special cases of the new entropy formula. Using the new entropy...

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Detalles Bibliográficos
Autores principales: Liu, Yujun, Ma, Guanzhong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10453602/
https://www.ncbi.nlm.nih.gov/pubmed/37628224
http://dx.doi.org/10.3390/e25081195
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author Liu, Yujun
Ma, Guanzhong
author_facet Liu, Yujun
Ma, Guanzhong
author_sort Liu, Yujun
collection PubMed
description A new variance formula is developed using the generalized inverse of an increasing function. Based on the variance formula, a new entropy formula for any uncertain variable is provided. Most of the entropy formulas in the literature are special cases of the new entropy formula. Using the new entropy formula, the maximum entropy distribution for unimodel entropy of uncertain variables is provided without using the Euler–Lagrange equation.
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spelling pubmed-104536022023-08-26 On the Entropy and the Maximum Entropy Principle of Uncertain Variables Liu, Yujun Ma, Guanzhong Entropy (Basel) Article A new variance formula is developed using the generalized inverse of an increasing function. Based on the variance formula, a new entropy formula for any uncertain variable is provided. Most of the entropy formulas in the literature are special cases of the new entropy formula. Using the new entropy formula, the maximum entropy distribution for unimodel entropy of uncertain variables is provided without using the Euler–Lagrange equation. MDPI 2023-08-11 /pmc/articles/PMC10453602/ /pubmed/37628224 http://dx.doi.org/10.3390/e25081195 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Liu, Yujun
Ma, Guanzhong
On the Entropy and the Maximum Entropy Principle of Uncertain Variables
title On the Entropy and the Maximum Entropy Principle of Uncertain Variables
title_full On the Entropy and the Maximum Entropy Principle of Uncertain Variables
title_fullStr On the Entropy and the Maximum Entropy Principle of Uncertain Variables
title_full_unstemmed On the Entropy and the Maximum Entropy Principle of Uncertain Variables
title_short On the Entropy and the Maximum Entropy Principle of Uncertain Variables
title_sort on the entropy and the maximum entropy principle of uncertain variables
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10453602/
https://www.ncbi.nlm.nih.gov/pubmed/37628224
http://dx.doi.org/10.3390/e25081195
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