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Generalized Entropies, Variance and Applications

The generalized cumulative residual entropy is a recently defined dispersion measure. In this paper, we obtain some further results for such a measure, in relation to the generalized cumulative residual entropy and the variance of random lifetimes. We show that it has an intimate connection with the...

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Autores principales: Toomaj, Abdolsaeed, Di Crescenzo, Antonio
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7517246/
https://www.ncbi.nlm.nih.gov/pubmed/33286481
http://dx.doi.org/10.3390/e22060709
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author Toomaj, Abdolsaeed
Di Crescenzo, Antonio
author_facet Toomaj, Abdolsaeed
Di Crescenzo, Antonio
author_sort Toomaj, Abdolsaeed
collection PubMed
description The generalized cumulative residual entropy is a recently defined dispersion measure. In this paper, we obtain some further results for such a measure, in relation to the generalized cumulative residual entropy and the variance of random lifetimes. We show that it has an intimate connection with the non-homogeneous Poisson process. We also get new expressions, bounds and stochastic comparisons involving such measures. Moreover, the dynamic version of the mentioned notions is studied through the residual lifetimes and suitable aging notions. In this framework we achieve some findings of interest in reliability theory, such as a characterization for the exponential distribution, various results on k-out-of-n systems, and a connection to the excess wealth order. We also obtain similar results for the generalized cumulative entropy, which is a dual measure to the generalized cumulative residual entropy.
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spelling pubmed-75172462020-11-09 Generalized Entropies, Variance and Applications Toomaj, Abdolsaeed Di Crescenzo, Antonio Entropy (Basel) Article The generalized cumulative residual entropy is a recently defined dispersion measure. In this paper, we obtain some further results for such a measure, in relation to the generalized cumulative residual entropy and the variance of random lifetimes. We show that it has an intimate connection with the non-homogeneous Poisson process. We also get new expressions, bounds and stochastic comparisons involving such measures. Moreover, the dynamic version of the mentioned notions is studied through the residual lifetimes and suitable aging notions. In this framework we achieve some findings of interest in reliability theory, such as a characterization for the exponential distribution, various results on k-out-of-n systems, and a connection to the excess wealth order. We also obtain similar results for the generalized cumulative entropy, which is a dual measure to the generalized cumulative residual entropy. MDPI 2020-06-26 /pmc/articles/PMC7517246/ /pubmed/33286481 http://dx.doi.org/10.3390/e22060709 Text en © 2020 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
Toomaj, Abdolsaeed
Di Crescenzo, Antonio
Generalized Entropies, Variance and Applications
title Generalized Entropies, Variance and Applications
title_full Generalized Entropies, Variance and Applications
title_fullStr Generalized Entropies, Variance and Applications
title_full_unstemmed Generalized Entropies, Variance and Applications
title_short Generalized Entropies, Variance and Applications
title_sort generalized entropies, variance and applications
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7517246/
https://www.ncbi.nlm.nih.gov/pubmed/33286481
http://dx.doi.org/10.3390/e22060709
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