Physical Sciences and Mathematics Commons^™

Linear Coordinate Systems And Statistical Independence And Vector Spaces And Linear Statistical Models, James B. Mcdonald

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The object of this report is an investigation of statistical independence and linear coordinate systems. It is hoped that this report will give some background for an ultimate investigation of independence and non­linear coordinate systems using tensor analysis.

An additional basic objective is to obtain explicit algebraic expressions for different types of linear trans- formations.

The first concepts to be covered are arbitrary linear transformations, various ways of looking at linear transformations, and the effects of a linear transformation on a vector of normally distributed random variables.

Next orthogonal transformations to independence, and then oblique transformations to independence will be …

Estimation Of Parameters Of Normal Populations From Truncated Samples, Kuo-Chung Liang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In statistical experiments, if a random sample of items drawn from a population is tested until all items fail, conventional statistical techniques may be employed but normal frequency distributions may not be satisfied. Failure of the data to satisfy the assumption of normality may lead to an invalid result. Some statistical results, however, have been shown to be robust to the failure of the data to meet normality. When using conventional experimental methods, considerable time and money are required to produce failure of all samples. To be economical, many experiments are concluded before all test items fail. A sample obtained …

Topics In Semigroups, Merlin Ray Jenson

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The semigroup theories of fundamental importance were discovered in 1928 with the publication of a paper by A. K. Suschkewitsch. The paper is included in the only book published prior to 1961 dealing primarily with the algebraic theory of semigroups. The book written by the above author and published in 1937 is entitles "The Theory of Generalized Groups."

Since 1940 the number of papers on semigroups has increased to approximately 30 per year. Thus we find ourselves in the midst of a new and expanding area of mathematics. Our interest centers around the structure of semigroups and their representation by …

Numerical Approximations To The Cumulative Chi-Square Distribution, The Cumulative T-Distribution And The Cumulative F-Distribution For Digital Computers, Grace Yuan-Chuen Wang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

There are good tables of the frequently used cumulative frequency distributions. These tables have some limitations with respect to the number of percentage points that are available. The main drawback in computer usage of these tables is that large amounts of storage and elaborate search and interpolation techniques are necessary for their use.

It is the purpose of this study to present associated numerical methods for digital computer which are satisfactorily accurate and which are reasonably economical in both time and machine memory capacity. To carry out this objective the following procedures were used:

1. A review of literature on …

An Exposition On Bayesian Inference, John Laffoon

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Bayesian approach to probability and statistics is described, a brief history of Bayesianism is related, differences between Bayesian and Frequentist schools of statistics are defined, protential applications are investigated, and a literature survey is presented in the form of a machine-sort card file.

Bayesian thought is increasing in favor among statisticians because of its ability to attack problems that are unassailable from the Frequentist approach. It should become more popular among practitioners because of the flexibility it allows experimenters and the ease with which prior knowledge can be combined with experimental data.