A New Sequential Goodness of Fit Test for the Three-Parameter Weibull Distribution with Known Shape Based on Skewness and Kurtosis.
AIR FORCE INST OF TECH WRIGHT-PATTERSONAFB OH SCHOOL OF ENGINEERING
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The Weibull distribution finds wide applicability across a broad spectrum of disciplines and is very prevalent in reliability theory. Consequently, numerous statistical tests have been developed to determine whether sample data can be adequately modeled with this distribution. Unfortunately, the majority of these goodness-of-fit tests involve a substantial degree of computational complexity. The study presented here develops and evaluates a new sequential goodness-of-fit test for the three-parameter Weibull distribution with a known shape that delivers power comparable to popular procedures while dramatically reducing computational requirements. The new procedure consists of two distinct tests, using only the sample skewness and sample kurtosis as test statistics. Critical values are derived using large Monte Carlo simulations for known shapes k0.50.54 and sample sizes n5550. Attained significance levels for all combinations of the two tests between alpha0.010.010.20 are also are approximated with Monte Carlo simulations and presented in a useful contour plot format. Extensive power studies against numerous alternate distributions demonstrate the tests excellent performance compared to popular EDF test statistics such as the Anderson-Darling and Cramer-von Mises tests. Recommendations are included on techniques to chose significance levels of the two component tests in a manner that should optimize power while maintaining the overall significance level.
- Statistics and Probability
- Operations Research