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Goodness-of-fit tests for the Weibull distribution based on the Laplace transform and Stein’s method

Author

Listed:
  • Bruno Ebner

    (Karlsruhe Institute of Technology (KIT))

  • Adrian Fischer

    (Université libre de Bruxelles (ULB))

  • Norbert Henze

    (Karlsruhe Institute of Technology (KIT))

  • Celeste Mayer

    (Landeskreditbank Baden-Württemberg – Förderbank (L-Bank))

Abstract

We propose novel goodness-of-fit tests for the Weibull distribution with unknown parameters. These tests are based on an alternative characterizing representation of the Laplace transform related to the density approach in the context of Stein’s method. Asymptotic theory of the tests is derived, including the limit null distribution, the behaviour under contiguous alternatives, the validity of the parametric bootstrap procedure, and consistency of the tests against a large class of alternatives. A Monte Carlo simulation study shows the competitiveness of the new procedure. Finally, the procedure is applied to real data examples taken from the materials science.

Suggested Citation

  • Bruno Ebner & Adrian Fischer & Norbert Henze & Celeste Mayer, 2023. "Goodness-of-fit tests for the Weibull distribution based on the Laplace transform and Stein’s method," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(6), pages 1011-1038, December.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:6:d:10.1007_s10463-023-00873-7
    DOI: 10.1007/s10463-023-00873-7
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    References listed on IDEAS

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    1. Gerrit Lodewicus Grobler & Elzanie Bothma & James Samuel Allison, 2022. "Testing for the Rayleigh Distribution: A New Test with Comparisons to Tests for Exponentiality Based on Transformed Data," Mathematics, MDPI, vol. 10(8), pages 1-17, April.
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    4. Steffen Betsch & Bruno Ebner, 2019. "A new characterization of the Gamma distribution and associated goodness-of-fit tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 779-806, October.
    5. James S. Allison & Steffen Betsch & Bruno Ebner & Jaco Visagie, 2022. "On Testing the Adequacy of the Inverse Gaussian Distribution," Mathematics, MDPI, vol. 10(3), pages 1-18, January.
    6. Alejandra Cabaña & Adolfo Quiroz, 2005. "Using the empirical moment generating function in testing for the Weibull and the type I extreme value distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 417-431, December.
    7. Steffen Betsch & Bruno Ebner, 2021. "Fixed point characterizations of continuous univariate probability distributions and their applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 31-59, February.
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