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Some properties and applications of cumulative Kullback–Leibler information

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  • Antonio Di Crescenzo
  • Maria Longobardi

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. Copyright © 2015 John Wiley & Sons, Ltd.

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  • Antonio Di Crescenzo & Maria Longobardi, 2015. "Some properties and applications of cumulative Kullback–Leibler information," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(6), pages 875-891, November.
    • Handle: RePEc:wly:apsmbi:v:31:y:2015:i:6:p:875-891
    DOI: 10.1002/asmb.2116
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    Cited by:

    1. E.I., Abdul Sathar & K.V., Viswakala, 2019. "Non-parametric estimation of Kullback–Leibler discrimination information based on censored data," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    2. Amit Ghosh & Chanchal Kundu, 2019. "Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures," Statistical Papers, Springer, vol. 60(6), pages 2225-2252, December.
    3. Maryam Eskandarzadeh & Antonio Di Crescenzo & Saeid Tahmasebi, 2019. "Cumulative Measure of Inaccuracy and Mutual Information in k -th Lower Record Values," Mathematics, MDPI, vol. 7(2), pages 1-19, February.

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