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Modified Goodness-Of-Fit Tests For The Weibull Distribution, Erol Yucel
Modified Goodness-Of-Fit Tests For The Weibull Distribution, Erol Yucel
Theses and Dissertations
This research will produce a new modified Anderson-Darling and W* goodness of fit statistics for the three parameter Weibull Distribution when all parameters unknown and estimated by Maximum Likelihood-Minimum Distance combination. The critical values for each statistic, sample size and a levels 0. 20, 0.15, 0.10, 0.05 and 0.01 are produced. The Monte Carlo Simulation used 5000 repetitions for sample sizes of 10, 15, 20, 25, 30, 40, and 50 with the Weibull shape equals to 3, scale equals to 4 and location equals to 10. The power study is made for the same sizes as above with the hypothesized …
A Modified Chi-Squared Goodness-Of-Fit Test For The Three-Parameter Gamma Distribution With Unknown Parameters, Thomas J. Sterle
A Modified Chi-Squared Goodness-Of-Fit Test For The Three-Parameter Gamma Distribution With Unknown Parameters, Thomas J. Sterle
Theses and Dissertations
A modified chi-squared goodness-of-fit test was created for the gamma distribution in the case where all three parameters must be estimated from the sample. Critical values are generated using a Monte Carlo simulation procedure with 5000 repetitions each. Random samples of 8 different sizes were drawn from gamma distributions with shape parameters 1, 1.5, 2., and 2.5. The shape, scale, and location parameters were then estimated from each sample, using an iterative technique combining the maximum likelihood and minimum distance methods, enabling, computation of the chi-squared statistics and critical values. The same process is used to generate random samples, parameter …
A Modified Anderson Darling Goodness-Of-Fit Test For The Gamma Distribution With Unknown Scale And Location Parameters, Tamer Ozmen
Theses and Dissertations
A new modified Anderson-Darling goodness-of-fit test is introduced for the three-parameter Gamma distribution when the location parameter is found by minimum distance estimation and scale parameter by maximum likelihood estimation. Monte Carlo simulation studies were performed to calculate the critical values for A-D test when A-D statistic is minimized. These critical values are then used for testing whether a set of observations follows a Gamma distribution when the scale and location parameters axe unspecified and are estimated from the sample. Functional relationship between the critical values of A-D is also examined for each shape parameter by the variables, sample size …