Weibull or not Weibull?

TL;DR

This paper introduces new goodness-of-fit tests for the Weibull distribution using a novel approach based on the Laplace transform and Stein's method, with strong theoretical backing and practical validation.

Contribution

It presents the first goodness-of-fit tests for Weibull distribution based on a new characterization involving the Laplace transform, with comprehensive asymptotic analysis and real data application.

Findings

Tests are asymptotically valid and consistent.

Monte Carlo simulations show competitive performance.

Application to materials science data demonstrates practical usefulness.

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.