Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Civil and Environmental Engineering

First Advisor

Donald Dean Adrian


A solution to a one dimensional diffusion equation applicable to a finite interval was adapted to be a probability distribution function. This distribution function can accommodate various shapes of distribution such as those similar to the uniform, single-modal, and bi-modal distributions. This distribution is bounded at both boundaries. It was named the finite Fourier distribution (FFD) to recognize the form of the distribution. The FFD was extended to include a linear combination of the FFD termed two-component FFD. Monte Carlo simulation technique was used to evaluate four parameter estimation techniques, Method of Maximum Likelihood Estimator (MLE), Method of Moments (MOM), Method of L-Moments (LMM), and Method of Least Square (LSQ). Robustness evaluation and other goodness-of-fit measures of these parameter estimation techniques are discussed. Both FFD and two-component FFD were applied to the field measured dissolved oxygen (DO) concentrations, laboratory measured hydraulic conductivity of clay liners, river quality data, and pore size distribution of compacted clays. Goodness-of-fit tests were performed to evaluate the models. The FFD provides similar or slightly better fit than the traditional distributions for certain sample data. Two-component FFD performed very well modeling the pore size distributions in compacted clays.