Accession Number : ADA115575

Title :   A Modified Cramer-von Mises and Anderson-Darling Test for the Weibull Distribution with Unknown Location and Scale Parameters.

Descriptive Note : Master's thesis,


Personal Author(s) : Bush,John Gregory

PDF Url : ADA115575

Report Date : Dec 1981

Pagination or Media Count : 156

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.

Descriptors :   *Weibull density functions, *Life tests, *Reliability, Air Force equipment, Value, Decision making, Samplers, Estimates, Parameters, Chi square test, Observation, Comparison, Test and evaluation, Statistical distributions, Monte Carlo method, Methodology, Theses

Subject Categories : Statistics and Probability
      Logistics, Military Facilities and Supplies

Distribution Statement : APPROVED FOR PUBLIC RELEASE