On empirical cumulative residual entropy and a goodness-of-fit test for exponentiality

Zardasht, Vali; Parsi, Safar; Mousazadeh, M.

doi:10.1007/s00362-014-0603-9

Cited by 21 publications

(11 citation statements)

References 19 publications

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“…Adding a tuning parameter to the weight function leads to the test statistic proposed by Baringhaus and Henze (2008). The recent papers by Cuparić et al (2018), Jovanović et al (2015), Nikitin (2017), Noughabi (2015), Torabi et al (2018), Volkova and Nikitin (2015), and Zardasht et al (2015) show that tests for exponentiality are still of importance to the research community.…”

Section: Tests For the Gamma Distributionmentioning

confidence: 99%

Fixed point characterizations of continuous univariate probability distributions and their applications

Betsch

Ebner

2019

Ann Inst Stat Math

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By extrapolating the explicit formula of the zero-bias distribution occurring in the context of Stein's method, we construct characterization identities for a large class of absolutely continuous univariate distributions. Instead of trying to derive characterizing distributional transformations that inherit certain structures for the use in further theoretic endeavours, we focus on explicit representations given through a formula for the density-or distribution function. The results we establish with this ambition feature immediate applications in the area of goodness-of-fit testing. We draw up a blueprint for the construction of tests of fit that include procedures for many distributions for which little (if any) practicable tests are known.To illustrate this last point, we construct a test for the Burr Type XII distribution for which, to our knowledge, not a single test is known aside from the classical universal procedures.MSC 2010 subject classifications. Primary 62E10 Secondary 60E10, 62G10Over the last decades, Stein's method for distributional approximation has become a viable tool for proving limit theorems and establishing convergence rates. At it's heart lies the well-known Stein characterization which states that a real-valued random variable Z has a standard normal distribution if, and only if,holds for all functions f of a sufficiently large class of test functions. To exploit this characterization for testing the hypothesisof normality, where P X is the distribution of a real-valued random variable X, against general alternatives, Betsch and Ebner (2019b) used that (1.1) can be untied from the class of test functions with the help of the so-called zero-bias transformation introduced by Goldstein and Reinert (1997). To be specific, a real-valued random variable X * is said to have the X-zero-bias distri-bution ifholds for any of the respective test functions f . If EX = 0 and Var(X) = 1, the X-zero-bias distribution exists and is unique, and it has distribution function(1.3)By (1.1), the standard Gaussian distribution is the unique fixed point of the transformation P X → P X * . Thus, the distribution of X is standard normal if, and only if,where F X denotes the distribution function of X. In the spirit of characterization-based goodnessof-fit tests, an idea introduced by Linnik (1962), this fixed point property directly admits a new class of testing procedures as follows. Letting T X n be an empirical version of T X and F n the empirical distribution function, both based on the standardized sample, Betsch and Ebner (2019b) proposed a test for (1.2) based on the statisticwhere w is an appropriate weight function, which, in view of (1.4), rejects the normality hypothesis for large values of G n . As these tests have several desirable properties such as consistency against general alternatives, and since they show a very promising performance in simulations, we devote this work to the question to what extent the fixed point property and the class of goodness-of-fit procedures may be generalized to othe...

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Section: Tests For the Gamma Distributionmentioning

confidence: 99%

Fixed point characterizations of continuous univariate probability distributions and their applications

Betsch

Ebner

2019

Ann Inst Stat Math

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“…The first test for exponentiality based on the CRE information measure considered is found in Zardasht et al (2015). Let X and Z be non-negative random variables with distribution functions F and G, respectively.…”

Section: Tests Based On Entropymentioning

confidence: 99%

“…If Z is also exponentially distributed, then it easily follows that C(W, Z) = 1 4 . The authors of Zardasht et al (2015) based their test statistic on the difference between an estimator for C(W, Z) and 1 4 . The resulting test statistic is thus The next test considered is based on the cumulative Kullback-Leibler (CKL) divergence (and indirectly on the CRE) introduced in Baratpour and Habibi Rad (2012).…”

Section: Tests Based On Entropymentioning

confidence: 99%

“…However, the most recent review paper on this topic was written more than 10 years ago by Henze and Meintanis (2005). Since then, a number of new tests have been proposed, see for example Jammalamadaka and Taufer (2006), Haywood and Khmaladze (2008), Mimoto and Zitikus (2008), Wang (2008), Volkova (2010), Grané and Fortiana (2011), Abbasnejad et al (2012), Baratpour and Habibi Rad (2012), Volkova and Nikitin (2013), Meintanis et al (2014), and Zardasht et al (2015). Furthermore, many of the tests for exponentiality contain a tuning parameter, often appearing in a weight function.…”

Section: Introductionmentioning

confidence: 99%

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An ‘apples to apples’ comparison of various tests for exponentiality

et al. 2017

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The exponential distribution is a popular model both in practice and in theoretical work. As a result, a multitude of tests based on varied characterisations have been developed for testing the hypothesis that observed data are realised from this distribution. Many of the recently developed tests contain a tuning parameter, usually appearing in a weight function. In this paper we compare the powers of 20 tests for exponentiality-some containing a tuning parameter and some that do not. To ensure a fair 'apples to apples' comparison between each of the tests, we employ a data-dependent choice of the tuning parameter for those tests that contain these parameters. The comparisons are conducted for various samples sizes and for a large number of alternative distributions. The results of the simulation study show that the test with the best overall power performance is the Baringhaus & Henze test, followed closely by the test by Henze & Meintanis; both tests contain a tuning parameter. The score test by Cox & Oakes performs the best among those tests that do not include a tuning parameter.

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“…In the complete sample case, numerous tests for testing the hypothesis that the observed data are realizations from the exponential distribution have been developed and studied. These include tests based on characteristic functions (Epps & Pulley, ; Meintanis, Swanepoel, & Allison, ), Laplace transforms (Baringhaus & Henze, ; Henze & Meintanis, ), mean residual life (Baringhaus & Henze, ; Jammalamadaka & Taufer, ), normalized spacings (Gnedenko, Belyayev, & Solovyev, ), and entropy (Zardasht, Parsi, & Mousazadeh, ; Baratpour & Rad, ) to name just a few. Furthermore, there are a multitude of properties that characterize the exponential distribution, see, for example, the monographs of Galambos and Kotz () and Kotz, Balakrishnan, and Johnson ().…”

Section: Introductionmentioning

confidence: 99%

Modified tests for exponentiality in the presence of Type II right censored data

Cockeran

Santana

Allison

2019

Stat

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The exponential distribution is one of the most popular choices of model, especially in survival analysis and reliability theory. Typically, to test the hypothesis that the underlying distribution of lifetimes are exponentially distributed based on censored data, the standard goodness‐of‐fit tests used in the complete sample case are modified. However, none of the characteristic or Laplace function based tests have been adapted to incorporate censored data. In this paper, we modify three well‐known tests for exponentiality on the basis of either the characteristic function or Laplace transform to accommodate Type II right censored data. We compare the power of the three newly changed tests to some existing modified tests in an independent identically distributed (i.i.d.) and a model‐based setup through a Monte Carlo study, where it was found that the newly adjusted Baringhaus and Henze test outperformed all other tests considered.

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On empirical cumulative residual entropy and a goodness-of-fit test for exponentiality

Cited by 21 publications

References 19 publications

Fixed point characterizations of continuous univariate probability distributions and their applications

Fixed point characterizations of continuous univariate probability distributions and their applications

An ‘apples to apples’ comparison of various tests for exponentiality

Modified tests for exponentiality in the presence of Type II right censored data

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