Asymptotic Expansions of the Distribution of Test Statistics Associated with Several Two Parameter Exponential Distributions

摘要

This thesis used three criteria to test for equality of p populations with underlying two parameter exponential distributions (theta = location parameter, sigma = scale parameter). The criteria use n random samples drawn for each of the p populations. The three criteria are based on three hypotheses. The asymptotic expansion of the distributions are found based on the Neyman-Pearson likelihood ratio. The asymptotic expansions are computed using Bernoulli polynomials and a recursive relationship developed by Kalinin and Shalaevskii. Nine tables of percentage points are computed for each test statistic from the expansions where p = 2(1)10, n = 10(1)20(5)50(10)100, and alpha = .100, 050, .025, .010, .005. These tables along with a practical illustration give the analyst a good technique that can be applied to many exponentially related situations.