Exact EDF Goodness-of-Fit Tests for Inverse Gaussian Distributions

Nguyen, Truc T.; Dinh, Khoan T.

doi:10.1081/sac-120017504

Cited by 5 publications

(4 citation statements)

References 10 publications

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“…The authors show that both procedures yield the same asymptotic null distribution. Exact edf tests for the IG2 were proposed by Nguyen and Dinh [12] but Gracia-Medrano and O'Reilly [13] showed that they have inferior power performance in small samples as compared with the tests of Edgeman et al [8] and O'Reilly and Rueda [11].…”

Section: Introductionmentioning

confidence: 99%

Cumulant plots and goodness-of-fit tests for the inverse Gaussian distribution

Koutrouvelis

Karagrigoriou

2012

Journal of Statistical Computation and Simulation

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This paper uses a standardized version of the logarithm of the empirical moment generating function in order to construct plots for assessing the appropriateness of the inverse Gaussian distribution. Variability is added to the plots by utilizing asymptotic and finite-sample results. The plots have linear scales and do not rely on the use of tables or special functions. In addition, they are equivalent to a goodness-of-fit test whose critical values are obtained from fitted equations involving the sample size and the estimated shape parameter of the inverse Gaussian distribution. Three data sets are used to illustrate the plots. A similar test is also proposed whose critical values are found through parametric bootstrap. An extensive simulation study shows that the new tests maintain good stability in level and high power across a wider range of distributions and sample sizes than other tests.

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Section: Introductionmentioning

confidence: 99%

Cumulant plots and goodness-of-fit tests for the inverse Gaussian distribution

Koutrouvelis

Karagrigoriou

2012

Journal of Statistical Computation and Simulation

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“…The methods by [8,9] are based on a characterization of the IG family by an independence property. In [10] a connection to the so-called random walk distribution is used, and [11] proposes exact tests based on the empirical distribution function of transformations characterizing the inverse Gaussian law, which are corrected in [12]. The author of [13] use a differential equation that characterizes the Laplace transform of the IG family as well as an L 2 -distance test, both using the empirical Laplace transform.…”

Section: Introductionmentioning

confidence: 99%

On Testing the Adequacy of the Inverse Gaussian Distribution

et al. 2022

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We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution based on a characterization of the cumulative distribution function (CDF). The new tests are of weighted L2-type depending on a tuning parameter. We develop the asymptotic theory under the null hypothesis and under a broad class of alternative distributions. These results guarantee that the parametric bootstrap procedure, which we employ to implement the test, is asymptotically valid and that the whole test procedure is consistent. A comparative simulation study for finite sample sizes shows that the new procedure is competitive to classical and recent tests, outperforming these other methods almost uniformly over a large set of alternative distributions. The use of the newly proposed test is illustrated with two observed data sets.

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“…This testing problem has been considered in the statistical literature. The methods by Baringhaus and Gaigall (2015) and Mudholkar et al (2001) are based on a characterization of the IG family by an independence property, Ducharme (2001) uses a connection to the so called Random Walk distribution, and Nguyen and Dinh (2003) propose exact tests based on the empirical distribution function of transformations characterising the inverse Gaussian law, which are commented and corrected in Gracia-Medrano and O'Reilly (2005). Henze and Klar (2002) use a differential equation that characterizes the Laplace transform of the IG family as well as a L 2 -distance test, both using the empirical Laplace transform.…”

Section: Introductionmentioning

confidence: 99%

New weighted $L^2$-type tests for the inverse Gaussian distribution

Allison,

Betsch,

Ebner

et al. 2019

Preprint

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We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution. The proposed tests are weighted L 2 -type tests depending on a tuning parameter. We develop the asymptotic theory under the null hypothesis and under a broad class of alternative distributions. These results are used to show that the parametric bootstrap procedure, which we employ to implement the test, is asymptotically valid and that the whole test procedure is consistent. A comparative simulation study for finite sample sizes shows that the new procedure is competitive to classical and recent tests, outperforming these other methods almost uniformly over a large set of alternative distributions. The use of the newly proposed test is illustrated with two observed data sets.

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Exact EDF Goodness-of-Fit Tests for Inverse Gaussian Distributions

Cited by 5 publications

References 10 publications

Cumulant plots and goodness-of-fit tests for the inverse Gaussian distribution

Cumulant plots and goodness-of-fit tests for the inverse Gaussian distribution

On Testing the Adequacy of the Inverse Gaussian Distribution

New weighted $L^2$-type tests for the inverse Gaussian distribution

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