Simplified likelihood based goodness-of-fit tests for the Weibull distribution

Meryam Krit (1, 2) , Olivier Gaudoin (1) , Min Xie (3) , Emmanuel Remy (2)

1 FIGAL - Fiabilité et Géométrie Aléatoire
2 EDF R&D MRI - Management des Risques Industriels
3 CUHK - City University of Hong Kong [Hong Kong]

The aim of this paper is to present new likelihood based goodness-of-fit tests for the two-parameter Weibull distribution. These tests consist in nesting the Weibull distribution in three-parameter generalized Weibull families and testing the value of the third parameter by using the Wald, score and likelihood ratio procedures. We simplify the usual likelihood based tests by getting rid of the nuisance parameters, using three estimation methods. The proposed tests are not asymptotic. A comprehensive comparison study is presented. Among a large range of possible GOF tests, the best ones are identified. The results depend strongly on the shape of the underlying hazard rate.

Mots clés: Likelihood ratio test; Goodness-of-fit tests; Weibull distribution; Extreme Value distribution; Reliability; Score test; Wald test

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Meryam Krit, Olivier Gaudoin, Min Xie, Emmanuel Remy. Simplified likelihood based goodness-of-fit tests for the Weibull distribution. Communications in Statistics - Simulation and Computation, 2016, 45 (3), pp.920-951. ⟨10.1080/03610918.2013.879889⟩. ⟨hal-00921267⟩