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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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