A wide review on exponentiality tests and two competitive proposals with application on reliability

Torabi, Hamzeh; Montazeri, Narges H.; Grané, Aurea

doi:10.1080/00949655.2017.1379522

Cited by 18 publications

(7 citation statements)

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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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“…We can see from tables that all the sizes of our tests are equal to the level of significance, and that the powers range from reasonable to high. In comparison to the other exponentiality tests (see [10] and [48]) we can conclude that our tests are serious competitors to the most powerful classical and recent exponentiality tests.…”

Section: Powers Of New Testsmentioning

confidence: 74%

New consistent exponentiality tests based on $V$-empirical Laplace transforms with comparison of efficiencies

Cuparić,

Milošević,

Obradović

2019

Preprint

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We present new consistent goodness-of-fit tests for exponential distribution, based on the Desu characterization. The test statistics represent the weighted L 2 and L ∞ distances between appropriate V-empirical Laplace transforms of random variables that appear in the characterization. In addition, we perform an extensive comparison of Bahadur efficiencies of different recent and classical exponentiality tests. We also present the empirical powers of new tests.

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Section: Tests Based On the Phi-divergence Measurementioning

confidence: 99%

“…In this paper we adapt the test of Torabi et al (2016) specifically for the Rayleigh distribution. Torabi et al (2016) suggested a new proximity measure which was inspired by the Phidivergence approach. This measure is used to develop a test for the location-scale family of distribution and specifically implemented to test for the normal distribution.…”

Section: Tests Based On the Phi-divergence Measurementioning

confidence: 99%

A Review of Goodness-of-Fit Tests for the Rayleigh Distribution

Liebenberg

Allison²

2023

AJS

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The Rayleigh distribution has recently become popular as a model for a range of phenomena. As a result, a number of goodness-of-fit tests have been developed for this distribution. In this paper, we provide the first overview of goodness-of-fit tests for the Rayleigh distribution and compare these tests in a Monte-Carlo study to identify the tests that provide the highest powers against a wide range of alternatives. Our findings suggest that two recently developed tests as well as a test based on the Laplace transform and a test based on the Hellinger distance are the better performing tests.

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A wide review on exponentiality tests and two competitive proposals with application on reliability

Cited by 18 publications

References 50 publications

Fixed point characterizations of continuous univariate probability distributions and their applications

Fixed point characterizations of continuous univariate probability distributions and their applications

New consistent exponentiality tests based on $V$-empirical Laplace transforms with comparison of efficiencies

A Review of Goodness-of-Fit Tests for the Rayleigh Distribution

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