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Open AccessArticle

Generalized Entropies, Variance and Applications

1
Department of Mathematics and Statistics, Faculty of Basic Sciences and Engineering, Gonbad Kavous University, Basirat Blvd., Shahid Fallahi Street, Gonbad Kavous 4971799151, Golestan Province, Iran
2
Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, I-84084 Fisciano (SA), Italy
*
Author to whom correspondence should be addressed.
The authors contributed equally to this work.
Entropy 2020, 22(6), 709; https://doi.org/10.3390/e22060709
Received: 23 May 2020 / Revised: 23 June 2020 / Accepted: 23 June 2020 / Published: 26 June 2020
(This article belongs to the Section Information Theory, Probability and Statistics)
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. View Full-Text
Keywords: generalized cumulative entropy; generalized cumulative residual entropy; variance; mean residual life; stochastic orders generalized cumulative entropy; generalized cumulative residual entropy; variance; mean residual life; stochastic orders
MDPI and ACS Style

Toomaj, A.; Di Crescenzo, A. Generalized Entropies, Variance and Applications. Entropy 2020, 22, 709.

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