Award Date

5-1-2015

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Committee Member

Malwane Ananda

Second Committee Member

Amie Amie

Third Committee Member

Hokwon Cho

Fourth Committee Member

Daniel Allen

Number of Pages

118

Abstract

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 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.

Keywords

Distribution (Probability theory); Generalized inference; Log-gamma distribution; Log-linear models; Log Pearson III; Multivariate analysis; Pivotal quantity; P values

Disciplines

Multivariate Analysis | Probability | Statistics and Probability

Language

English


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