Residual and Past Discrete Tsallis and Renyi Extropy with an Application to Softmax Function

In this paper, based on the discrete lifetime distribution, the residual and past of the Tsallis and Renyi extropy are introduced as new measures of information. Moreover, some of their properties and their relation to other measures are discussed. Furthermore, an example of a uniform distribution o...

Descripción completa

Detalles Bibliográficos
Autores principales: Jawa, Taghreed M., Fatima, Nahid, Sayed-Ahmed, Neveen, Aldallal, Ramy, Mohamed, Mohamed Said
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9777819/
https://www.ncbi.nlm.nih.gov/pubmed/36554137
http://dx.doi.org/10.3390/e24121732
_version_ 1784856200814264320
author Jawa, Taghreed M.
Fatima, Nahid
Sayed-Ahmed, Neveen
Aldallal, Ramy
Mohamed, Mohamed Said
author_facet Jawa, Taghreed M.
Fatima, Nahid
Sayed-Ahmed, Neveen
Aldallal, Ramy
Mohamed, Mohamed Said
author_sort Jawa, Taghreed M.
collection PubMed
description In this paper, based on the discrete lifetime distribution, the residual and past of the Tsallis and Renyi extropy are introduced as new measures of information. Moreover, some of their properties and their relation to other measures are discussed. Furthermore, an example of a uniform distribution of the obtained models is given. Moreover, the softmax function can be used as a discrete probability distribution function with a unity sum. Thus, applying those measures to the softmax function for simulated and real data is demonstrated. Besides, for real data, the softmax data are fit to a convenient ARIMA model.
format Online
Article
Text
id pubmed-9777819
institution National Center for Biotechnology Information
language English
publishDate 2022
publisher MDPI
record_format MEDLINE/PubMed
spelling pubmed-97778192022-12-23 Residual and Past Discrete Tsallis and Renyi Extropy with an Application to Softmax Function Jawa, Taghreed M. Fatima, Nahid Sayed-Ahmed, Neveen Aldallal, Ramy Mohamed, Mohamed Said Entropy (Basel) Article In this paper, based on the discrete lifetime distribution, the residual and past of the Tsallis and Renyi extropy are introduced as new measures of information. Moreover, some of their properties and their relation to other measures are discussed. Furthermore, an example of a uniform distribution of the obtained models is given. Moreover, the softmax function can be used as a discrete probability distribution function with a unity sum. Thus, applying those measures to the softmax function for simulated and real data is demonstrated. Besides, for real data, the softmax data are fit to a convenient ARIMA model. MDPI 2022-11-27 /pmc/articles/PMC9777819/ /pubmed/36554137 http://dx.doi.org/10.3390/e24121732 Text en © 2022 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
Jawa, Taghreed M.
Fatima, Nahid
Sayed-Ahmed, Neveen
Aldallal, Ramy
Mohamed, Mohamed Said
Residual and Past Discrete Tsallis and Renyi Extropy with an Application to Softmax Function
title Residual and Past Discrete Tsallis and Renyi Extropy with an Application to Softmax Function
title_full Residual and Past Discrete Tsallis and Renyi Extropy with an Application to Softmax Function
title_fullStr Residual and Past Discrete Tsallis and Renyi Extropy with an Application to Softmax Function
title_full_unstemmed Residual and Past Discrete Tsallis and Renyi Extropy with an Application to Softmax Function
title_short Residual and Past Discrete Tsallis and Renyi Extropy with an Application to Softmax Function
title_sort residual and past discrete tsallis and renyi extropy with an application to softmax function
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9777819/
https://www.ncbi.nlm.nih.gov/pubmed/36554137
http://dx.doi.org/10.3390/e24121732
work_keys_str_mv AT jawataghreedm residualandpastdiscretetsallisandrenyiextropywithanapplicationtosoftmaxfunction
AT fatimanahid residualandpastdiscretetsallisandrenyiextropywithanapplicationtosoftmaxfunction
AT sayedahmedneveen residualandpastdiscretetsallisandrenyiextropywithanapplicationtosoftmaxfunction
AT aldallalramy residualandpastdiscretetsallisandrenyiextropywithanapplicationtosoftmaxfunction
AT mohamedmohamedsaid residualandpastdiscretetsallisandrenyiextropywithanapplicationtosoftmaxfunction

Ejemplares similares