Doubly truncated (interval) cumulative residual and past entropy

Khorashadizadeh, Mohammad; Roknabadi, A. H. Rezaei; Borzadaran, Gholam Reza Mohtashami

doi:10.1016/j.spl.2013.01.033

Cited by 26 publications

(14 citation statements)

References 16 publications

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“…When g(x) = f (x), we obtain interval entropy of X in (t 1 , t 2 ) studied by Sunoj et al (2009) and Yari (2011, 2012), among others. Recently, for doubly truncated random variables Khorashadizadeh et al (2013) introduced the concepts of interval cumulative residual entropy (ICRE) as…”

Section: Some Properties Of Interval Cri and Cpimentioning

confidence: 99%

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On cumulative residual (past) inaccuracy for truncated random variables

Kundu

Crescenzo

Longobardi

2015

Metrika

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To overcome the drawbacks of Shannon's entropy, the concept of cumulative residual and past entropy has been proposed in the information theoretic literature. Furthermore, the Shannon entropy has been generalized in a number of different ways by many researchers. One important extension is Kerridge inaccuracy measure. In the present communication we study the cumulative residual and past inaccuracy measures, which are extensions of the corresponding cumulative entropies. Several properties, including monotonicity and bounds, are obtained for left, right and doubly truncated random variables

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Section: Some Properties Of Interval Cri and Cpimentioning

confidence: 99%

“…The following theorem shows that there exist no nonnegative random variables for which ICRI is increasing over the domain D. We omit the proof, being similar to that of Theorem 2.2 of Khorashadizadeh et al (2013).…”

mentioning

confidence: 96%

On cumulative residual (past) inaccuracy for truncated random variables

Kundu

Crescenzo

Longobardi

2015

Metrika

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“…Other results on dynamic discrimination measures based on the Kullback–Leibler information have been provided by Khorashadizadeh et al . , Kumar et al . , Navarro et al .…”

Section: Introductionmentioning

confidence: 99%

Some properties and applications of cumulative Kullback–Leibler information

Crescenzo

Longobardi

2015

Appl Stoch Models Bus & Ind

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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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“…Similarly, the interval cumulative residual (past) entropy has been introduced by Khorashadizadeh et al (2013). Moreover, Kundu and Nanda (2015) defined and studied the interval inaccuracy measure.…”

Section: Is Clear That Ih(x; 0 T) = Pe(x; T) and Ih(x; T ∞) = Re(x;mentioning

confidence: 99%

Some Characterization Results on Dynamic Cumulative Past Inaccuracy Measure

Khorashadizadeh

2018

JIRSS

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Abstract. In this paper, borrowing the intuition in Rao et al. (2004), we introduce a cumulative version of the inaccuracy measure (CIM). Also we obtain interesting and applicable properties of CIM for different cases based on the residual, past and interval lifetime random variables. Relying on various applications of stochastic classes in reliability and information theory fields, we study new classes of the lifetime in terms of the CIM along with their relations with other famous aging classes. Furthermore, some characterization results are obtained under the proportional reversed hazard rate model. Finally, considering that the time t changes in the range (t 1 , t 2 ), an extension of the CIM, called the interval cumulative residual (past) inaccuracy (ICR(P)I), is derived. We investigate the ICRI's relation with its analogous version based on Shannon entropy.

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Doubly truncated (interval) cumulative residual and past entropy

Cited by 26 publications

References 16 publications

On cumulative residual (past) inaccuracy for truncated random variables

On cumulative residual (past) inaccuracy for truncated random variables

Some properties and applications of cumulative Kullback–Leibler information

Some Characterization Results on Dynamic Cumulative Past Inaccuracy Measure

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