Physical Sciences and Mathematics Commons^™

U. S. U. Mathematical Programming Package, R. Gary Goodwin

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

Solving mathematical programming problems without the aid of electronic computers is very time consuming even for a mathematical model consisting of only a few constraints and variables. The objective of this report is to illustrate the use of mathematical programming computer routines available at Utah State University. Computer routines discussed are the International Business Machines (IBM), Mathematical Programming System (MPS) package, a quadratic programming routing, a zero-one integer programming routing, and a transportation code. The MPS package is a product of IBM; the quadratic programming routing was develop by the author: the last three routines were obtained from the IBM …

A Monte Carlo Evaluation Of A Nonparametric Technique For Estimating The Hazard Function, Sheng Jia Lin

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

This research is primarily concerned with the estimation of the Hazard functions, the Hazard function is the failure rate at time t, and is defined as -R '(t)/R(t), so it plays an important role in Reliability.

In order to compare and evaluate the estimation methods, it is convenient to select one distribution in this research. Since the Weibull distribution is a useful distribution in Reliability, the Weibull distribution is used in this paper.

Torus Knots, David S. Bradley

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

We have compiled here many interesting results concerning a particular collection of knots called torus knots. Torus knots are merely simple closed curves imbedded in an unknotted torus T² in E³. We show that the fundamental groups of T², π(T²), is the direct product of the additive group of integers with itself. The ordered pair (p, q) in Z x Z determines an equivalence class of loops on the torus, and we show in Section II that the class [(p, q)] contains a loop whose image is a simple closed curve if and …

A Bayes Rule For The Symmetric Multiple Comparisons Problem, Aban Nawabi

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

Many procedures have been proposed for the symmetric multiple comparisons problem in recent years. These include a "protected" least significant difference procedure due to Fisher (FSD), a multiple range rule by Duncan, and HSD (honest significant difference) procedure by Tukey, and a procedure for testing all contrasts by Scheffe.

The tests which are mentioned above are either comparison-wise or experiment-wise approaches. The probability of Type I error is intended to be a for all comparisons made when an experiment-wise approach is used. Whereas, the probability of Type I error referred to each comparison is a comparison-wise approach. Both approaches can …

A Non-Parametric Sequential Signed-Rank Test And Comparison With The Sequential T-Test, Kuei-Mei Even Sher

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

Sequential analysis is a method of statistical inference whose characteristic feature is that the number of observations required by the procedure is not determined in advance of the experiment. The decision to terminate the experiment depends, at each stage, on the results of the observations previously made.

So far the general sequential t-test (without truncation) is a standard test for the mean of a normal distribution. A truncated sequential t-test has been developed by Suich and Iglewicz (1970). The difference between these two tests is that the former has a fixed critical value whenever the type I error (α) and …