Testing Goodness-of-Fit for Exponential Distribution Based on Cumulative Residual Entropy

Baratpour, S.; Rad, A. Habibi

doi:10.1080/03610926.2010.542857

Cited by 104 publications

(75 citation statements)

References 17 publications

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“…Ebrahimi et al [13] based on the sample entropy fitted the exponential distribution for the data successfully. Recently, the same conclusion has been drawn by Baratpour and Habibi Rad [6].…”

Section: Examplesupporting

confidence: 64%

Testing Exponentiality Based on the Likelihood Ratio and Power Comparison

Noughabi

2015

Ann. Data. Sci.

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The exponential distribution is one of the fundamental lifetime models and is widely used for describing a failure mechanism of a system. Different applications of this distribution in survival analysis and reliability theory can be found in statistical literature. In this article, some powerful tests for exponentiality based on the likelihood ratio are proposed. The critical points of the test statistics are obtained by Monte Carlo simulations. The power values of the proposed tests are computed against a wide variety of alternative hypotheses and then these values are compared with the power values of the recent published exponentiality tests. It is shown that these tests have a reasonable power for various kinds of departures from exponentiality. For illustrative purpose, real examples are finally presented.

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Section: Examplesupporting

confidence: 64%

Testing Exponentiality Based on the Likelihood Ratio and Power Comparison

Noughabi

2015

Ann. Data. Sci.

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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%

“…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%

“…Some extensions of KL information have been studied by some authors including Park (2012), Park and Shin (2013) for the Type I censored distribution and Balakrishnan et al (2007) for the Type II progressively censored distribution. Barapour and Rad (2012) recently suggested a cumulative residual KL information, an extension of KL information to the survival function, as…”

Section: Scaled Cumulative Residual Kl Informationmentioning

confidence: 99%

“…Kullback-Leibler (KL) information is defined for f (x) and g(x) being the reference distribution as KL(g : f ) = ∞ −∞ Barapour and Rad (2012) suggested the cumulative residual KL information (CRKL) for the nonnegative random variable, which is well-defined on the empirical distribution function, as…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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Entropic Kullback‐Leibler type distance measures for quantum distributions

Laguna

Salazar

Sagar

2019

Int J of Quantum Chemistry

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Entropic distance measures for quantum mechanical probability distributions, which are characterized by nodal structure and symmetry holes, are considered. We illustrate how the Kullback-Leibler (KL) distance is not well defined in some instances and propose instead the use of the cumulative residual Kullback-Leibler (CRKL) distance.The KL and CRKL measures are compared and contrasted for some representative quantum mechanical systems: The particle in an infinite well, the harmonic oscillator, and hydrogenic systems. We present cases where CRKL can be used to obtain distances whereas KL cannot be used, and also highlight examples where the KL and CRKL measures yield different behaviors and interpretations. An extension of the CRKL definition is obtained for application to harmonic oscillator systems defined over [−∞, ∞]. Distance measures for two-variable (particle) distributions are also considered to address generalizations of the mutual information correlation measure.The use of CRKL in measuring distances between orbitals is also discussed. K E Y W O R D S cumulative residual Kullback-Leibler entropy, Kullback-Leibler, quantum distributions, relative entropy

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Testing Goodness-of-Fit for Exponential Distribution Based on Cumulative Residual Entropy

Cited by 104 publications

References 17 publications

Testing Exponentiality Based on the Likelihood Ratio and Power Comparison

Testing Exponentiality Based on the Likelihood Ratio and Power Comparison

On scaled cumulative residual Kullback-Leibler information

Entropic Kullback‐Leibler type distance measures for quantum distributions

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