A Ratio-Type Goodness-of-Fit Test for 2-Parameter Weibull Distributions

This paper extends Gnedenko´s F (ratio) test for exponentiality to the 2-parameter Weibull distribution. When the shape parameter is known, a Weibull distribution can be reduced to an exponential by a suitable transformation, and then one can test the hypothesis that a given sample could have come from the specific Weibull population using the F procedure. However, when the true values of the parameters are not known, a technique for estimating these values must be selected before any goodness-of-fit test can be performed. We have selected various estimators for the shape, transformed accordingly, and then derived and tabulated critical values for Gnedenko´s ratio statistic in each case. The key result is that the convergence-in-distribution of the test statistic to the F distribution is most rapid when the Menon estimator is used.