Anderson-Darling and Cramer-Von Mises Based Goodness-of-Fit Tests for the WeibullDistribution With Known Shape Using Normalized Spacings

摘要

Two new goodness-of-fit tests are developed for the three-parameter Weibulldistribution with known shape parameter. These procedures eliminate the need for estimating the unknown location and scale parameters prior to initiating the tests and are easily adapted for censored data. This is accomplished by employing the Anderson-Darling and Cramer-von Mises statistics based on the normalized spacings of the sample data. Critical values of the new tests are obtained for common significance levels by large Monte Carlo simulations for shapes 0.5(0.5)4.0 and sample sizes 5(5)40 with up to 40% censoring (Type II) from the left and/or right. An extensive Monte Carlo power study is also conducted to compare the two tests with each other and with their prominent competitors. The competitors include another spacings test, Z*, and the modified Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling EDF tests. Results show the Anderson-Darling spacings test is the preferred test for the three-parameter Weibull distribution with known shape parameter.