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.
翻译：我们建议对Weibull的分布进行新的、有未知参数的完善测试,这些测试基于与Stein方法中密度法有关的Laplace变异的描述的替代特征,从中得出了测试的零分配限制、毗连替代物的行为、参数靴带程序的有效性、对大量替代物的测试的一致性。蒙特卡洛模拟研究表明了新程序的竞争力。最后,该程序适用于从材料科学中提取的真实数据实例。
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