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

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, inc...

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Bibliographic Details
Published in:Annals of the Institute of Statistical Mathematics 2023-12, Vol.75 (6), p.1011-1038
Main Authors: Ebner, Bruno, Fischer, Adrian, Henze, Norbert, Mayer, Celeste
Format: Article
Language:English
Subjects:
Asymptotic methods
Economics
Finance
Goodness of fit
Insurance
Laplace transforms
Management
Materials science
Mathematics
Mathematics and Statistics
Monte Carlo simulation
Statistical tests
Statistics
Statistics for Business
Weibull distribution
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Summary: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.
ISSN:0020-3157
1572-9052
DOI:10.1007/s10463-023-00873-7