A Modified Cramer-von Mises and Anderson-Darling Test for the Weibull Distribution with Unknown Location and Scale Parameters.
Abstract
The Anderson-Darling and Cramer-von Mises critical values are generated for the three-parameter Weibull distribution. The critical values are used for testing whether a set of observations follows a Weibull distribution when the scale and location parameters are unspecified and are estimated from the sample. A Monte Carlo simulation, with 5000 repetitions, is used to generate critical values for sample sizes 5(5)30 and Weibull shape parameter .5(.5)4.0. A Monte Carlo power investigation of the Anderson-Darling and Cramer-von Mises tests is made using 5, 15, and 25 observations from ten alternate distributions. The power of the two tests are compared to the Kolmogorov-Smirnov and the Chi-Square tests. The power of all the tests are low with a sample size of five. When the hypothesized distribution is the Weibull with shape equal 1.0, the power of the tests in decreasing order are: Cramer-von Mises, Anderson-Darling, Kolmogorov-Smirnov, and Chi-Square. When the hypothesized distribution is the Weibull with shape equal 3.5, the power of the tests are the Anderson-Darling, followed by the Cramer-von Mises, Kolmogorov-Smirnov, and the Chi-Square test.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1981
- Accession Number
- ADA115575
Entities
People
- John Gregory Bush
Organizations
- Air Force Institute of Technology