A Goodness-of-Fit Test for a Family of Two Parameter Weibulls with Known Shape Using Minimum Distance Estimation of Parameters
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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This research is to produce a modified Anderson-Darling goodness of fit test for the Weibull distribution when the location parameter is found by minimum distance estimation, the shape parameter is assumed known, and the MLE is used for the scale parameter. The critical values for the Anderson-Darling test are generated via Monte Carlo simulation when both the Anderson-Darling and Cramer-Von Mises distance statistics are minimized. These critical values are then used for a power study. The Monte Carlo simulation used 5000 repetitions for sample sizes of 5,8,12,15,16,20 and 25 with the Weibull shape parameter of . 5.54.0. The power study is made for the same sample sizes as above with the hypothesized Weibull shape parameter of 1.0 and 3.5 against ten alternate hypothesized distributions. For small sample sizes, improvement can be seen over tests which use MLEs for the location and scale parameters. However, for larger sample sizes, more than 20, the power is similar to other goodness-of-fit tests for the Weibull. In most cases, minimizing the Anderson-Darling distance statistic to estimate the Weibull location parameter had more power than minimizing the Cramer-Von Mises distance statistic.
- Statistics and Probability