A Monte Carlo Simulation study of goodness-of-fit tests for Weibull distribution based on the empirical distribution function

The Weibull distribution is widely used in reliability as a model for time to failure. In this paper, we investigate goodness-of-fit tests based on the empirical distribution function and apply them to test the validity of the Weibull model. We use the maximum likelihood estimator to estimate the scale and shape parameters of the distribution.  A Monte Carlo simulation study is employed to determine the critical values and the actual size of the considered tests. The power values of the tests are computed and compared with each other.  A real data example is used to illustrate the proposed tests.