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

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Abstract
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.