Modified Goodness-of-Fit Test for the Lognormal Distribution with Unknown Scale and Location Parameters

摘要

This thesis developed modified goodness-of-fit tests for the three parameter lognormal distribution when the location and scale parameters must be estimated from the sample. The critical values were generated for the Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises goodness-of-fit tests, using the Monte Carlo methods of 5000 repetitions, to simulate samples of size 5,10,...,30 and the second part of the research also involved a Monte Carlo simulation of 5000 repetitions for sample sizes of 5,15, and 25. From these observations, the power of the test was determined by counting the number of times the modified goodness-of-fit tests incorrectly accepted null hypothesis that the distribution was lognormally distributed. The data used in this power comparison came from the lognormal distribution (shape = 1.0 and 3.0), Weibull, gamma, beta, exponential, and normal distributions. The third and and final phase of research was to determine the functional relationship, in any, between the known shape parameter and the new modified critical values. This was completed by using SAS.