6533b852fe1ef96bd12aa354

RESEARCH PRODUCT

Generalized Entropies, Variance and Applications

Abdolsaeed ToomajAntonio Di Crescenzo

subject

Reliability theory62B10Exponential distributionGeneral Physics and AstronomyPoisson processlcsh:Astrophysicsstochastic orders02 engineering and technologyResidualvariance01 natural sciencesArticle62N05010104 statistics & probabilitysymbols.namesakelcsh:QB460-4660202 electrical engineering electronic engineering information engineeringApplied mathematics60E050101 mathematicsgeneralized cumulative entropylcsh:ScienceResidual entropyGeneralized cumulative entropy; Generalized cumulative residual entropy; Variance; Mean residual life; Stochastic ordersMathematics94A17generalized cumulative residual entropymean residual lifelcsh:QC1-999stochastic orders.symbols020201 artificial intelligence & image processinglcsh:Qlcsh:Physics

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.

yearjournalcountryeditionlanguage
2020-06-26Entropy
10.3390/e22060709https://www.mdpi.com/1099-4300/22/6/709