The cumulative Kullback-Leibler information has been proposed recently as a suitable extension of Kullback-Leibler information to the cumulative distribution function. In this paper we obtain various results on such a measure, with reference to its relation with other information measures and notions of reliability theory. We also provide some lower and upper bounds. A dynamic version of the cumulative Kullback-Leibler information is then proposed for past lifetimes. Furthermore, we investigate its monotonicity property, which is related to some new concepts of relative aging. Moreover, we propose an application to the failure of nanocomponents. Finally, in order to provide an application in image analysis we introduce the empirical cumulative Kullback-Leibler information and prove an asymptotic result.

Some properties and applications of cumulative Kullback-Leibler information

DI CRESCENZO, Antonio;
2015

Abstract

The cumulative Kullback-Leibler information has been proposed recently as a suitable extension of Kullback-Leibler information to the cumulative distribution function. In this paper we obtain various results on such a measure, with reference to its relation with other information measures and notions of reliability theory. We also provide some lower and upper bounds. A dynamic version of the cumulative Kullback-Leibler information is then proposed for past lifetimes. Furthermore, we investigate its monotonicity property, which is related to some new concepts of relative aging. Moreover, we propose an application to the failure of nanocomponents. Finally, in order to provide an application in image analysis we introduce the empirical cumulative Kullback-Leibler information and prove an asymptotic result.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4587458
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