Abstract
Abdelfattah et al. [2] had estimated the parameters of the 2-Weibull distribution using Bayesian estimation. Abdelfattah [1] had estimated the Weibull density using goodness of fit tests. The estimation of the Weibull density is now introduced by parametric methods. Some numerical results were obtained through a simulation study to obtain the critical values for some well known statistics, beside the power function for these tests.