Statistics and Probability Commons^™

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.

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 …

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.

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 Μ-Model Approach On The Cell Means: The Analysis Of Full, Design Models With Non-Orthogonal Data, Richard Van Koningsveld

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This work considers the application of a µ-model approach on the cell means to a special yet important class of experimental designs. These include full factorial, completely nested, and mixed models with one or more observations per cell. By limiting attention to full models, an approach to the general data situation is developed which is both conceptually simple and computationally advantageous.

Conceptually, the method is simple because the design related effects are defined as if the cell means are single observations. This leads to a rather simple algorithm for generating main effect contrasts, from which associated interaction contrasts can also …

The Prior Distribution In Bayesian Statistics, Kai-Tang Chen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A major problem associated with Bayesian estimation is selecting the prior distribution. The more recent literature on the selection of the prior is reviewed. Very little of a general nature on the selection of the prior is formed in the literature except for non-informative priors. This class of priors is seen to have limited usefulness. A method of selecting an informative prior is generalized in this thesis to include estimation of several parameters using a multivariate prior distribution. The concepts required for quantifying prior information is based on intuitive principles. In this way, it can be understood and controlled by …

Estimation Of Floods When Runoff Originates From Nonhomogeneous Sources, David Ray Olson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Extreme value theory is used as a basis for deriving a distribution function for flood frequency analysis when runoff originates from nonhomogeneous sources. A modified least squares technique is used to estimate the parameters of the distribution function for eleven rivers. Goodness-of-fit statistics are computed and the distribution function is found to fit the data very well.

The derived distribution function is recommended as a base method for flood frequency analysis for rivers exhibiting nonhomogeneous sources of runoff if further investigation also proves to be positive.

Multicollinearity And The Estimation Of Regression Coefficients, John Charles Teed

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The precision of the estimates of the regression coefficients in a regression analysis is affected by multicollinearity. The effect of certain factors on multicollinearity and the estimates was studied. The response variables were the standard error of the regression coefficients and a standarized statistic that measures the deviation of the regression coefficient from the population parameter.

The estimates are not influenced by any one factor in particular, but rather some combination of factors. The larger the sample size, the better the precision of the estimates no matter how "bad" the other factors may be.

The standard error of the regression …

Interpretation Of Principal Components, Marwan A. Dabdoub

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The principal component analysis can be carried out two ways. First the R-mode:

R = K'K

and the second is the Q-mode:

Q = K K'

where K is a data matrix centered by column or by row. The most commonly used method is the R-mode.

It has been suggested that principal components computed from either the R-mode or the Q-mode may have the same interpretation. If this is true, then interpretation of the principal components could be put on a much more intuitive level in many applications. This will occur whenever one type of principal component …

An Evaluation Of Truncated Sequential Test, Ryh-Thinn Chang

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The development of sequential analysis has led to the proposal of tests that are more economical in that the Average Sample Number (A. S. N.) of the sequential test is smaller than the sample size of the fixed sample test. Although these tests usually have a smaller A. S. N. than the equivelent fixed sample procedure, there still remains the possibility that an extremely large sample size will be necessary to make a decision. To remedy this, truncated sequential tests have been developed.

A method of truncation for testing a composite hypotheses is studied. This method is formed by mixing …

A Study Of Four Statistics, Used In Analysis Of Contingency Tables, In The Presence Of Low Expected Frequencies, Jane R. Post

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Four statistics used for the analysis of categorical data were observed in the presence of many zero cell frequencies in two way classification contingency tables. The purpose of this study was to determine the effect of many zero cell frequencies upon the distribution properties of each of the four statistics studied. It was found that Light and Margolin's C and Pearson's Chi-square statistic closely approximated the Chi-square distribution as long as less than one-third of the table cells were empty. It was found that the mean and variance of Kullbach's 2I were larger than the expected values in the presence …

Comparison Of Transition Matrices Between Metropolitan And Non-Metropolitan Areas In The State Of Utah Using Juvenile Court Data, Sung-Ik Song

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to use Markov Chains for the study of youths referred to the juvenile court in the metropolitan and non-metropolitan areas of the state of Utah.

Two computer programs were written for creating case histories for each person referred to the court and for testing for the significance of the difference among several transition matrices.

Another computer program, which was written by Soo Hong Uh, was used for analyzing realizations of a Markov chains up to the 4th order; a third computer program, originally written by David White, was used for interpreting Markov chains.

The …

A Comparative Analysis Of The Use Of A Markov Chain Versus A Binomial Probability Model In Estimating The Probability Of Consecutive Rainless Days, Jack Wilfred Homeyer

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Markov chain process for predicting the occurence of a sequence of rainless days, a standard technique, is critically examined in light of the basic underlying assumptions that must be made each time it is used. This is then compared to a simple binomial model wherein an event is defined to be a series of rainless days of desired length. Computer programs to perform the required calculations are then presented and compared as to complexity and operating characteristics. Finally, an example of applying both programs to real data is presented and further comparisons are drawn between the two techniques.

Analysis Of Case Histories By Markov Chains Using Juvenile Court Data Of State Of Utah, Soo-Hong Uh

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to analyze juvenile court data using Markov Chains. A computer program was generalized with a single array orientation for analyzing realizations of a Markov Chain to the k^th order within machine limitations. The data used in this paper were gathered by the Juvenile Court of the State of Utah for administrative purposes and limited to District II. The results from the paper, "Statistical Inference About Markov Chains" by Anderson and Goodman, were applied for testing hypotheses. The paper is divided into five chapters: introduction, statistical background, methodology, analysis and summary, conclusions.

An Investigation Of Cluster Analysis, John C. Klingel

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Three cluster analysis programs were used to group the same 64 individuals, generated so as to represent eight populations of eight individuals each. Each individual had quantitative values for seven attributes. All eight populations shared a common attribute variance-covariance matrix.

The first program, from F. J. Rohlf's MINT package, implemented single linkage. Correlation was used as the basis for similarity. The results were not satisfactory, and the further use of correlation is in question.

The second program, MDISP, bases similarity on Euclidean distance. It was found to give excellent results, in that it clustered individuals into the exact populations from …

Sequential Analysis For Tolerances Of Noxious Weed Seeds, Seung Tokko

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The application of a sequential test, the sequential probability ratio test, for the tolerances of noxious weed seeds is studied. It is proved that the sequential test can give a similar power curve to that of the current fixed sample test if the test parameters are properly chosen.

The average sample size required by a sequential test, in general, is smaller than that of the existing test. However, in some cases it requires relatively a larger sample than current test.

As a solution to the problem a method of truncation is considered. A kind of mixed procedure is suggested. This …

Selecting The Best Linear Model From A Subset Of All Possible Models For A Given Set Of Predictors In A Multiple Linear Regression Analysis, David L. Jensen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Sixteen "model building" and "model selection" procedures commonly encountered in industry, all of which were initially alleged to be capable of identifying the best model from the collection of 2^k possible linear models corresponding to a given set of k predictors in a multiple linear regression analysis, were individually summarized and subsequently evaluated by considering their comparative advantages and limitations from both a theoretical and a practical standpoint. It was found that none of the proposed procedures were absolutely infallible and that several were actually unsuitable. However, it was also found that most of these techniques could still be …

A Two Sample Test Of The Reliability Performance Of Equipment Components, Miki Lynne Coleman

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this study was to develop a test which can be used to compare the reliability performances of two types of equipment components to determine whether or not the new component satisfies a given feasibility criterion.

Two types of tests were presented and compared: the fixed sample size test and the truncated sequential probability ratio test. Both of these tests involve use of a statistic which is approximately distributed as F.

This study showed that the truncated sequential probability ratio test has good potential as a means of comparing two component types to see whether or not the …

Fitting Some Families Of Contagious Distributions To Biological And Accident Data, Yung-Sung Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Four families of contagious distributions--generalized Poisson distributions, generalized binomial distributions, generalized Pascal distributions, and generalized log-zero distributions--are investigated in this thesis.

The family of generalized Poisson distributions contains five distributions: the Neyman Type A, the "Short," the Poisson binomial, the Poisson Pascal, and the negative binomial. The family of generalized binomial distributions contains eight distributions: the binomial Poisson, the binomial binomial, the binomial Pascal, the binomial log-zero, the Poisson with zeros, the binomial with zeros, the Pascal with zeros, and the log-zero with zeros. The family of generalized Pascal distributions contains four distributions: the Pascal Poisson, the Pascal binomial, the …

Resource Requirements Determination (Based On Statistical Methods), Robert L. Howard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Two methods of determining resource requirements at an Air Force maintenance depot were developed.

The first method is designed for new workloads and is based on infinite queuing theory formulas. Tables have been developed for this method.

The second method is designed for workload with, at minimum, several months of historical data. An optimum fit test was designed to aid in fitting and smoothing the empirical data to the normal distribution. These data are then input to simulation model for determination of resource requirements.

Statistical Analysis For Tolerances Of Noxious Weed Seeds, Yadolah Dodge

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

An analysis of the previous method for testing tolerances of noxious weed seeds was performed. Problems of the current techniques were discussed, and the solution to these problems was given.

A new technique of testing through the sequential test ratio was developed, and results examined.

The sequential test was found to be useful enough to include the use of it in determining tolerances for noxious weed seeds.

This study did show that the use of sequential tests does have excellent potential and flexibility as a statistical tool for the tolerances of noxious weed seeds.

The Effectiveness Of Categorical Variables In Discriminant Function Analysis, Preston Jay Waite

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A preliminary study of the feasibility of using categorical variables in discriminant function analysis was performed. Data including both continuous and categorical variables were used and predictive results examined.

The discriminant function techniques were found to be robust enough to include the use of categorical variables.

Some problems were encountered with using the trace criterion for selecting the most discriminating variables when these variables are categorical. No monotonic relationship was found to exist between the trace and the number of correct predictions.

This study did show that the use of categorical variables does have much potential as a statistical tool …

A Fortran List Processor (Flip), Karl A. Fugal

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A series of Basic Assembler Language subroutines were developed and made available to the FORTRAN IV language processor which makes list processing possible in a flexible and easily understood way.

The subroutine will create and maintain list structures in the computer's core storage. The subroutines are sufficiently general to permit FORTRAN programmers to tailor list processing routines to their own individual requirements. List structure sizes are limited only by the amount of core storage available.

Model For Bathtub-Shaped Hazard Rate: Monte Carlo Study, Glen S. Leithead

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A new model developed for the entire bathtub-shaped hazard rate curve has been evaluated as to its usefulness as a method of reliability estimation. The model is of the form:

F(t) = 1 - exp - (ϴ₁t^L + ϴ₂t + ϴ₃t^M)

where "L" and "M" were assumed known.

The estimate of reliability obtained from the new model was compared with the traditional restricted sample estimate for four different time intervals and was found to have less bias and variance for all time points.

This was a monte carlo study and the …

A Report On The Statistical Properties Of The Coefficient Of Variation And Some Applications, Howard P. Irvin

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Examples from four disciplines were used to introduce the coefficient of variation which was considered to have considerable usage and application in solving Quality Control and Reliability problems.

The statistical properties were found in the statistical literature and are presented, namely, the mean and the variance of the coefficient of variation. The cumulative probability function was determined by two approximate methods and by using the noncentral t distribution. A graphical method to determine approximate confidence intervals and a method to determine if the coefficients of variation from two samples were significantly different from each other are also provided (with examples). …

Analysis Of Contingency Tables, James Joseph Biundo

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Two methods of analyzing multi-dimensional frequency data are detailed.

The Second Order Exponential (SOE) model is applicable for dichotomous classifications. The distribution has two sets of parameters, ϴ_i's and ϴ_j's. The ϴ_i's are interpreted as the log of the odds of the marginal probabilities if no two factor relationships exist. Or if all ϴ_ij are not zero, then the ϴ_i's are analogous to a main effect in a 2^m factorial analysis, (m = number of factors or classifications). The ϴ_if's may be interpreted as a measure and direction …

Generation Of Random Numbers, Keith H. Eberhard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Subroutines are written to generate random numbers on the computer. Depending on the subroutine used, the generated random numbers follow the uniform, binomial, normal, chi-square, t, F, or gamma distribution. Each subroutine is tested using the chi-square goodness of fit test to verify that the random numbers generated by each subroutine follow the statistical distribution for which it is written. The interpretation of the test results indicates that each subroutine generates random numbers which closely approximates the theoretical distribution for which it is designed.

The approach used in the subroutine which generates gamma distributed random numbers involves the use of …

Rational Arithmetic As A Means Of Matrix Inversion, Jay Roland Peterson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The solution to a set of simultaneous equations is of the form A^-1 B = X where A^-1 is the inverse of A in the equation AX= B. The purpose of this study is to obtain an exact A^-1 through the use of rational arithmetic, and to study the behavior of rational numbers when used in arithmetic calculations.

This study describes a matrix inversion program written in SPS II, utilizing the concept of rational arithmetic. This program, using the Gaussian elimination matrix inversion method, is compared to the same method written in Fortran. Gaussian elimination …

Design Optimization Using Model Estimation Programming, Richard Kay Brimhall

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Model estimation programming provides a method for obtaining extreme solutions subject to constraints. Functions which are continuous with continuous first and second derivatives in the neighborhood of the solution are approximated using quadratic polynomials (termed estimating functions) derived from computed or experimental data points. Using the estimating functions, an approximation problem is solved by a numerical adaptation of the method of Lagrange. The method is not limited by the concavity of the objective function.

Beginning with an initial array of data observations, an initial approximate solution is obtained. Using this approximate solution as a new datum point, the coefficients for …

Fortran Programs For The Calculation Of Most Of The Commonly Used Experimental Design Models, H. Wain Greenhalgh

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Two computer programs were developed using a CDC 3100. They were written in FORTRAN IV.

One program uses four tape drives, one card reader, and one printer. It will calculate factorial analysis of variance with or without covariance and/or multivariate analysis for one to eight factors and up to twenty-five variables.

The other program is used for completely randomized designs, randomized block designs, and latin square designs. It will handle twenty-five treatments, rows (blocks), and columns. The program can handle fifteen variables using any number of these variables for covariates.