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

被引：1

作者：

Ebner, Bruno ^{[1
]}

Fischer, Adrian ^{[2
]}

Henze, Norbert ^{[1
]}

Mayer, Celeste ^{[3
]}

机构：

[1] Karlsruhe Inst Technol KIT, Inst Stochast, Englerstr 2, D-76133 Karlsruhe, Germany

[2] Univ libre Bruxelles ULB, Campus Plaine-CP 210,Blvd Triomphe,ACC2, B-1050 Brussels, Belgium

[3] Landeskreditbank Baden Wurttemberg Forderbank L Ba, Schlosspl 21, D-76131 Karlsruhe, Germany

来源：

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 2023年 / 75卷 / 06期

关键词：

Goodness-of-fit; Weibull distribution; Hilbert-space valued random elements; Contiguous alternatives; EXTREME-VALUE; PARAMETER; STATISTICS;

D O I：

10.1007/s10463-023-00873-7

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：1011 / 1038

页数：28

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