Goodness-of-fit tests for the Weibull distribution based on the Laplace transform

Résumé

The aim of this paper is to develop new goodness-of-fit (GOF) tests for the two-parameter Weibull distribution based on the Laplace transform. The principle of the tests relies on the measure of the closeness between the theoretical Laplace transform and its empirical version. Three estimation methods are used to simplify the building of the statistics. The paper also introduces a new version of Caba\~{n}a and Quiroz statistic using the maximum likelihood estimators of the parameters. All these tests are not asymptotic and can be used for small samples size. A comprehensive comparison study is presented. Among all the proposed GOF tests, the best ones are identified. The results strongly depend on the shape of the underlying hazard rate.