An Entropy Formulation Based on the Generalized Liouville Fractional Derivative

This paper presents a new formula for the entropy of a distribution, that is conceived having in mind the Liouville fractional derivative. For illustrating the new concept, the proposed definition is applied to the Dow Jones Industrial Average. Moreover, the Jensen-Shannon divergence is also general...

Descripción completa

Detalles Bibliográficos
Autores principales: Ferreira, Rui A. C., Tenreiro Machado, J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515131/
https://www.ncbi.nlm.nih.gov/pubmed/33267352
http://dx.doi.org/10.3390/e21070638
_version_ 1783586748396208128
author Ferreira, Rui A. C.
Tenreiro Machado, J.
author_facet Ferreira, Rui A. C.
Tenreiro Machado, J.
author_sort Ferreira, Rui A. C.
collection PubMed
description This paper presents a new formula for the entropy of a distribution, that is conceived having in mind the Liouville fractional derivative. For illustrating the new concept, the proposed definition is applied to the Dow Jones Industrial Average. Moreover, the Jensen-Shannon divergence is also generalized and its variation with the fractional order is tested for the time series.
format Online
Article
Text
id pubmed-7515131
institution National Center for Biotechnology Information
language English
publishDate 2019
publisher MDPI
record_format MEDLINE/PubMed
spelling pubmed-75151312020-11-09 An Entropy Formulation Based on the Generalized Liouville Fractional Derivative Ferreira, Rui A. C. Tenreiro Machado, J. Entropy (Basel) Article This paper presents a new formula for the entropy of a distribution, that is conceived having in mind the Liouville fractional derivative. For illustrating the new concept, the proposed definition is applied to the Dow Jones Industrial Average. Moreover, the Jensen-Shannon divergence is also generalized and its variation with the fractional order is tested for the time series. MDPI 2019-06-28 /pmc/articles/PMC7515131/ /pubmed/33267352 http://dx.doi.org/10.3390/e21070638 Text en © 2019 by the authors. 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 (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Ferreira, Rui A. C.
Tenreiro Machado, J.
An Entropy Formulation Based on the Generalized Liouville Fractional Derivative
title An Entropy Formulation Based on the Generalized Liouville Fractional Derivative
title_full An Entropy Formulation Based on the Generalized Liouville Fractional Derivative
title_fullStr An Entropy Formulation Based on the Generalized Liouville Fractional Derivative
title_full_unstemmed An Entropy Formulation Based on the Generalized Liouville Fractional Derivative
title_short An Entropy Formulation Based on the Generalized Liouville Fractional Derivative
title_sort entropy formulation based on the generalized liouville fractional derivative
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515131/
https://www.ncbi.nlm.nih.gov/pubmed/33267352
http://dx.doi.org/10.3390/e21070638
work_keys_str_mv AT ferreiraruiac anentropyformulationbasedonthegeneralizedliouvillefractionalderivative
AT tenreiromachadoj anentropyformulationbasedonthegeneralizedliouvillefractionalderivative
AT ferreiraruiac entropyformulationbasedonthegeneralizedliouvillefractionalderivative
AT tenreiromachadoj entropyformulationbasedonthegeneralizedliouvillefractionalderivative

Ejemplares similares