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

摘要

This research presents a new sequential goodness of fit test for the three-parameter gamma distribution with a known shape. The test is accomplished by employing two new tests, sample skewness and sample kurtosis, sequentially as test statistics. Unlike the typical goodness of fit test, using parameter estimation methods such as maximum likelihood estimation and minimum distance estimation, this test using the two test statistics above does not involve a substantial degree of computational complexity. Large Monte Carlo simulation has been used to determine critical values and overall significance levels for all combinations of the two tests, and to conduct extensive power studies against a broad range of alternatives. The results have been compared with those of popular EDF tests such as the Anderson-Darling, Cramer-von Mises, and Komogrov- Smirov tests. The comparative study demonstrated the sequential tests superiority over a broad range of alternatives. Hence, with computational efficiency and good power properties, the new sequential test is powerful enough to be utilized in the goodness of fit test field.