Date of Award
Master of Science
Department of Mathematics and Statistics
John S. Crown, PhD
Due to its flexibility, the Weibull distribution has very wide applicability in a lot of disciplines and is very prevalent in reliability theory. Thus, a lot of statistical tests that generally have a substantial degree of computational complexity have been developed to determine if the data at hand can be represented with this distribution. This research presents a new omnibus goodness-of-fit test (G.O.F.) that has less computational complexity than the existing tests for the three-parameter Weibull distribution using a sequential application of two individual tests, sample skewness and Q-Statistic. A Monte Carlo procedure has been employed to generate critical values for the skewness and Q-Statistic (G.O.F.) tests for various Weibull distributions with specified shape parameter values. Additionally, tables or charts of attained significance levels for the new sequential G.O.F. test procedure have been generated. Using the critical values and significance levels, a sequential G.O.F. test procedure can be used to determine if the given sample data agrees with a hypothesized Weibull distribution with known shape. A power study has been conducted against a variety of alternative hypotheses, and the results were compared with those obtained using conventional EDF type Cramer-von Mises, Ahderson-Darling and Kolmogorov-Smimov G.O.F tests, and the sequential procedure by Clough. Since the sequential test demonstrates better or equivalent power, it serves to significantly reduce the computational requirements for powerful G.O.F. testing.
DTIC Accession Number
Memis, Tibet, "A New Sequential Goodness-Of-Fit-Test for the Three-Parameter Weibull Distribution with Known Shape Parameter Value Based on Skewness and Q-Statis G.O.F. Test Statistics" (1999). Theses and Dissertations. 5303.