Using the Empirical Moment Generating Function in Testing for the Weibull and the Type I Extreme Value Distributions

We introduce a family of statistics, based on the empirical moment generating function, for testing goodness of fit to the two-parameter Weibull distribution or, equivalently, to the type I extreme value model. The asymptotic distribution of these statistics correspond to functionals of an appropriate gaussian limiting process. For one of the statistics considered, we estimate, via simulations, some of its sample quantiles, as well as the power of the statistic against some alternatives of interest