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

被引：0
作者：
Bruno Ebner
Adrian Fischer
Norbert Henze
Celeste Mayer
机构：
[1] Karlsruhe Institute of Technology (KIT),Institute of Stochastics
[2] Université libre de Bruxelles (ULB),undefined
[3] Landeskreditbank Baden-Württemberg – Förderbank (L-Bank),undefined
来源：
Annals of the Institute of Statistical Mathematics | 2023年 / 75卷
关键词：
Goodness-of-fit; Weibull distribution; Hilbert-space valued random elements; Contiguous alternatives;
D O I：
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中图分类号：
学科分类号：
摘要：
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.
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页码：1011 / 1038
页数：27
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