Physical Sciences and Mathematics Commons^™

Evaluation Of Multivariate Homogenous Arma Model, Lucy Chienhua Tseng

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis is to study a restricted multivariate AFRMA model, called the Homogeneous Model. This model is defined as one in which each univariate component of the multivariate model is of the same order in p and q as it is in the multivariate model.

From a mathematical respect, multivariate ARMA model is homogeneous if, and only if, its coefficient matrices are diagonal. From a physical respect, the present observation of a phenomenon can be modeled only by its own past observation and its present and past "errors."

The estimation procedures are developed based on maximum likelihood …

Extreme Value Distribution In Hydrology, Bill (Tzeng-Lwen) Chen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The problems encountered when empirical fit is used as the sole criterion for choosing a distribution to represent annual flood data are discussed. Some theoretical direction is needed for this choice. Extreme value theory is established as a viable tool for analyzing annual flood data. Extreme value distributions have been used in previous analyses of flood data. However, no systematic investigation of the theory has previously been applied. Properties of the extreme value distributions are examined. The most appropriate distribution for flood data has not previously been fit to such data. The fit of the chosen extreme value distribution compares …

A Confidence Interval Estimate Of Percentile, How Coung Jou

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The confidence interval estimate of percentile and its applications were studied. The three methods of estimating a confidence interval were introduced. Some properties of order statistics were reviewed. The Monte Carlo Method -- used to estimate the confidence interval was the most important one among the three methods. The generation of ordered random variables and the estimation of parameters were discussed clearly. The comparison of the three methods showed that the Monte Carlo method would always work, but the K-S and the simplified methods would not.

Exact Analysis Of Variance With Unequal Variances, Noriaki Yanagi

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper was to present the exact analysis of variance with unequal variances. Bishop presented the new procedure for the r-way layout ANOVA. In this paper, one and two way layout ANOVA were explained and Bishop's method and Standard method were compared by using a Monte Carlo method.