Search results for "Cumulative entropy"

showing 2 items of 2 documents

Fractional generalized cumulative entropy and its dynamic version

2021

Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with distributions satisfying the proportional reversed hazard model. We study the connection with fractional integrals, and some bounds and comparisons based on stochastic orderings, that allow to show that the proposed measure is actually a variability measure. The investigation also involves various notions of reliability theory, since the considered dynamic measure is a suitable extension of the mean inactivity time. We also introduce the empirical generalized fract…

FOS: Computer and information sciencesExponential distributionComputer Science - Information TheoryMathematics - Statistics TheoryStatistics Theory (math.ST)01 natural sciencesMeasure (mathematics)010305 fluids & plasmas0103 physical sciencesFOS: MathematicsApplied mathematicsAlmost surelyCumulative entropy; Fractional calculus; Stochastic orderings; EstimationEntropy (energy dispersal)010306 general physicsStochastic orderingsMathematicsCentral limit theoremNumerical AnalysisInformation Theory (cs.IT)Applied MathematicsCumulative distribution functionProbability (math.PR)Fractional calculusEmpirical measureFractional calculusModeling and SimulationEstimationCumulative entropyMathematics - ProbabilityCommunications in Nonlinear Science and Numerical Simulation
researchProduct

Generalized Entropies, Variance and Applications

2020

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 resul…

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:PhysicsEntropy
researchProduct