New Modified Anderson-Darling and Cramer-Von Mises Goodness-of-Fit Tests for a Normal Distribution with Specified Parameters
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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This thesis improves the powers of the Anderson-Darling and Cramer-von Mises goodness-of-fit tests using the mean rank and the median rank plotting positions. A Monte Carlo simulation of 5000 repetitions is used to generate the critical values from n 4 through n 80 for certain significance levels. An extensive power study is performed to compare the powers of the modified tests to the known tests for the uniform, the exponential, the double exponential, the lognormal, and the Weibull distributions. The power of the A-D tests modified by the median rank plotting and the mean rank plotting position are approximately 0.01 higher than the unmodified tests. The power of the C-VM test is 10 higher than the unmodified C-VM test for the Weibull, the lognormal, the exponential, and the double exponential distributions when the median rank plotting position also improves the power of the C-VM test for the uniform and the Weibull distributions while it reduces the power for the exponential, the double exponential, and the lognormal distributions.
- Statistics and Probability