Exact Statistical Inferences for Functions of Parameters of the Log-Gamma Distribution

Abstract

Exact Statistical Inferences for Functions of Parameters of the Log-Gamma Distribution by Joseph McDonald Malwane Ananda, Examination Committee Chair Professor of Mathematical Sciences University of Nevada, Las Vegas The log-gamma model has been used extensively for flood frequency analysis and is an important distribution in reliability, medical and other areas of lifetime testing. Conventional methods fails to provide exact solutions for the log-gamma model while asymptotic methods provide approximate solutions that often have poor performance for typical sample sizes. The two parameter log-gamma distribution is examined using the generalized p-value approach. The methods are exact in the sense that the tests and the confidence intervals are based on exact probability statements rather than on asymptotic approximations. Exact tests and exact confidence intervals for the parameter of interest based on a generalized test statistic will be used to compute generalized p-values which can be viewed as extensions to classical p-values. The generalized approach is compared to the classical approach using simulations and published studies. The Type I error and confidence intervals of these exact tests are iii often better than the performance of more complicated approximate tests obtained by standard methods reported in literature. Statistical inference for the mean, variance and coefficient of variance of the log-gamma distribution are given, and the performances of these procedures over the methods reported in the literature are compared using Monte Carlo simulations.