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

Bruno Ebner (), Adrian Fischer, Norbert Henze and Celeste Mayer
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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)

Annals of the Institute of Statistical Mathematics, 2023, vol. 75, issue 6, No 6, 1038 pages

Abstract: 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.

Keywords: Goodness-of-fit; Weibull distribution; Hilbert-space valued random elements; Contiguous alternatives (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10463-023-00873-7

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