Simplified Likelihood Based Goodness-of-fit Tests for the Weibull Distribution

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.