A New Sequential Goodness of Fit Test for the Three-Parameter Gamma Distribution With Known Shape Based on Skewness and Kurtosis

This research presents a sequential goodness of fit test for the three-parameter gamma distribution with a known shape. The test is accomplished by employing the two new tests, sample skewness and sample kurtosis, sequentially as test statistics. Unlike the typical goodness of fits using parameter estimation methods such as MLE (maximum likelihood estimation) and MD (minimum distance estimation). This sequential goodness of fit tests using two test statistics above do not involve a substantial degree of computational complexity. Critical values are obtained using large Monte Carlo simulations, which use ’percentile’ function, for shapes of 0.5(0.5)4.0 and sample sizes of 5(5)50. Attained significance levels for all combinations of the two tests between = 0:01(0:01)0:20 are also approximated with Monte Carlo simulations. Extensive power studies are then conducted against two sets of alternatives. One is against common alternative distributions and the other is comparative study whose competitor are popular EDF test statistics such as the Anderson-Darling, Cramer-von Mises, and Komogrov-Smirove tests.

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