On cumulative residual Kullback–Leibler information

Park, Sangun; Rao, Murali; Shin, Dong Wan

doi:10.1016/j.spl.2012.06.015

Cited by 71 publications

(53 citation statements)

References 13 publications

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“…is the cumulative Kullback-Leibler information introduced by Park et al (2012) and Di Crescenzo and Longobardi (2015). Moreover, we have…”

Section: Introduction and Preliminary Resultsmentioning

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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“…is the cumulative Kullback-Leibler information introduced by Park et al (2012) and Di Crescenzo and Longobardi (2015). Moreover, we have…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

Some Characterization Results on Dynamic Cumulative Past Inaccuracy Measure

Khorashadizadeh

2018

JIRSS

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“…In this paper, we considered some estimates of the scaled CRKL and study the performance as a goodness of the fit test statistic for an exponential distribution, which include the test statistics in Barapour and Rad (2012), and Park et al (2012). As a result, we found that the performance of the sCRKL test statistic varies much according to the chosen parameter estimators.…”

Section: Resultsmentioning

confidence: 99%

“…The second one is the method of moment estimator based on the second moment, which also minimizes CRKL θ . The third one is the estimator considered in Baratpour and Rad (2012), and the fourth one is the estimator considered in Park et al (2012).…”

Section: Scaled Cumulative Residual Kl Informationmentioning

confidence: 99%

“…We will consider sixteen combinations, sCRKLλ ,θ , which include the test statistics in Barapour and Rad (2012), and Park et al (2012). The critical values of sixteen test statistics for a sample of size 20 are obtained with the Monte Carlo simulation, where the simulation size is 100000, and are tabulated in Table 2.…”

Section: Power Comparisons and Unbiasednessmentioning

confidence: 99%

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On scaled cumulative residual Kullback-Leibler information

Hwang¹,

Park²

2013

Journal of the Korean Data and Information Science Society

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Cumulative residual Kullback-Leibler (CRKL) information is well defined on the empirical distribution function (EDF) and allows us to construct a EDF-based goodness of fit test statistic. However, we need to consider a scaled CRKL because CRKL is not scale invariant. In this paper, we consider several criterions for estimating the scale parameter in the scale CRKL and compare the performances of the estimated CRKL in terms of both power and unbiasedness.

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“…Further work in this area with similar concepts was done by [80,81], using the notation cumulative residual Kullback-Leiber (CRKL) information and cumulative Kullback-Leiber (CKL) information.…”

Section: Cumulative Paired φ-Divergencementioning

confidence: 99%

Cumulative Paired φ-Entropy

Klein

Mangold

Doll

2016

Entropy

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Abstract:A new kind of entropy will be introduced which generalizes both the differential entropy and the cumulative (residual) entropy. The generalization is twofold. First, we simultaneously define the entropy for cumulative distribution functions (cdfs) and survivor functions (sfs), instead of defining it separately for densities, cdfs, or sfs. Secondly, we consider a general "entropy generating function" φ, the same way Burbea et al. (IEEE Trans. Inf. Theory 1982, 28, 489-495) and Liese et al. (Convex Statistical Distances; Teubner-Verlag, 1987) did in the context of φ-divergences. Combining the ideas of φ-entropy and cumulative entropy leads to the new "cumulative paired φ-entropy" (CPE φ ). This new entropy has already been discussed in at least four scientific disciplines, be it with certain modifications or simplifications. In the fuzzy set theory, for example, cumulative paired φ-entropies were defined for membership functions, whereas in uncertainty and reliability theories some variations of CPE φ were recently considered as measures of information. With a single exception, the discussions in the scientific disciplines appear to be held independently of each other. We consider CPE φ for continuous cdfs and show that CPE φ is rather a measure of dispersion than a measure of information. In the first place, this will be demonstrated by deriving an upper bound which is determined by the standard deviation and by solving the maximum entropy problem under the restriction of a fixed variance. Next, this paper specifically shows that CPE φ satisfies the axioms of a dispersion measure. The corresponding dispersion functional can easily be estimated by an L-estimator, containing all its known asymptotic properties. CPE φ is the basis for several related concepts like mutual φ-information, φ-correlation, and φ-regression, which generalize Gini correlation and Gini regression. In addition, linear rank tests for scale that are based on the new entropy have been developed. We show that almost all known linear rank tests are special cases, and we introduce certain new tests. Moreover, formulas for different distributions and entropy calculations are presented for CPE φ if the cdf is available in a closed form.

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On cumulative residual Kullback–Leibler information

Cited by 71 publications

References 13 publications

Some Characterization Results on Dynamic Cumulative Past Inaccuracy Measure

Some Characterization Results on Dynamic Cumulative Past Inaccuracy Measure

On scaled cumulative residual Kullback-Leibler information

Cumulative Paired φ-Entropy

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