Robert T. Gorman

Goodness of Fit (GOF) tests for non-location/scale families of distributions have not been studied extensively. Previous research has focused on the case where the distribution function is either completely specified or a member of a location/scale family. A new test statistic, which resembles a regression sum of squares, is developed and its properties investigated in this dissertation. This statistic is shown to converge to a central chi-squared random variable under the null hypothesis, even for non-location/scale hypotheses. Hence, the test statistic is asymptotically distribution free. Conditions for which the procedure is consistent are developed. Also, Sequences of Local Alternatives (SLA's) to the null distribution are defined. It is shown that the distribution of the test statistic under these SLA's is a non-central chi-squared random variable. Presently, there exist only a few competing procedures for testing non-location/scale null hypotheses. Further, no small sample studies exist for this case. Therefore, a Monte Carlo study was performed to evaluate the power of the test procedure, its suitability for use with finite sample sizes, and, lastly, to compare it to its only practical competitor. These results indicate that this is a viable procedure with moderate sample sizes and that its power is greater than that of its only practical competitor.