Applied Statistics Commons^™

The Evaluation Of Glasser's Maximum Likelihood Method On Missing Data In Regression, Gayle M. Yamasaki

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

Missing data in regression is often a problem to research workers because standard regression methods are applicable only to complete data sets. At present there are three general methods for solving the problem of missing data.

At first, the reduced data method, reduces the incomplete data set to a complete data set before analyzing. Although this method is very simple to apply, substantial amounts of information are sometimes lost when data is eliminated. This results in less precise estimates of the regression parameters.

The second method, generalized least squares, estimates the missing values through least squares techniques, thus obtaining a …

Integer Programming By Cutting Planes Methods, Sung-Yen Wu

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

Linear programming is a relatively new, very important branch of modern mathematics and is about twenty five years old.

In this day and age, most planners and decision makers will acknowledge that some linear optimization problems are worth the expense and trouble to solve. Using linear programming technique as a tool to make decision plannes are able to greatly redice cost or increase profit for any project under consideration.

Since Dr. George B. Dantzig published his first paper on the simplex method in 1947, progress in that field has been rapid. Although the first applications were military in nature, it …

A Nonparametric Solution For Finding The Optimum Useful Life Of Equipment, Barry T. Stoll

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

It is often the case that equipment used by industry must be replaced with new equipment from time to time either because frequent malfunctions make it too costly to repair, or because the equipment has simply worn out. The new equipment often has the nature of either malfunctioning soon after installation due to manufacturing defects, or functioning for an extended period of time because it is free of these defects. For this reason, equipment is often given a preliminary running called the burn-in which gives no useful output but merely tests for manufacturing defects. Also, after a given amount of …

Canonical Analysis Of Several Sets Of Variables, Chong S. Kim

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

Many procedures have been proposed for analyzing and describing multivariate dependence structure.

Partial correlation, multiple correlation, canonical correlation, principal component and factor analysis are used to analyze the dependence structures of a multinormal population.

For a partial correlation analysis it is necessary to decide which variables are to be correlated and which of the remaining variables must be held constant.

Multiple correlation demands that one variable be dependent upon some or all of the remaining variates.

For a canonical correlation, the variables must be collected into two or more sets. The factor analysis technique is for explaining the covariances of …

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.

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 …

Nonparametric Test Of Fit, Frena Nawabi

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

Most statistical methods require assumptions about the populations from which samples are taken. Usually these methods measure the parameters, such as variance, standard deviations, means, etc., of the respective populations. One example is the assumption that a given population can be approximated closely with a normal curve. Since these assumptions are not always valid, statisticians have developed several alternate techniques known as nonparametric tests. The models of such tests do not specify conditions about population parameters.

Certain assumptions, such as (1) observations are independent and (2) the variable being studied has underlying continuity, are associated with most nonparametric tests. However, …

Solutions Of The Problem Of Finding Confidence Intervals For The Two Normal Population With Unequal Variances, Ing-Haur Liu

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

Comparison of the means of two normal populations is a simpler problem when the variance (if unknown) are assumed to be equal than it is when they are not equal. The main concern of this report is the latter case also called the Behrens [4] - Fisher [5] problem.

In this report the solutions proposed by Behrens-Fisher, Scheffe [10], Welch [12], Banerjee [3] and Hajek [8], will be described and compared. To this problem Scheffe proposed a solution which has the advantage that no special table is necessary for its use, since the variate has an exact "Student's t" distribution. …

The Practical Solutions And Computer Program Of Two Statistical Problems In Simulation, Yee Fong

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

In the last several years monte-carlo simulation has become a major tool for the analysis of complex queuing systems which are no readily amenable to analysis by conventional mathematical methods. By a complex queueing system is mean a system composed of, physically or by analogy, a network of stations or servers with traffic units moving through all or some of the servers, into the system and out or around within the system. A traffic unit desiring service by a server may either have to enter a queue first or may be served immediately. Such systems have been simulated often with …

Partially Balanced Incomplete Block Designs, Yaw-Tarng Shih

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

In balanced incomplete block designs, each pair of treatments is compared with equal precision, and each treatment is paired with every other treatment an equal number of times with in a common block; A is a constant for all treatments. There is one associate class for each treatment in balanced incomplete block designs. These are the most important balanced incomplete block designs, but the need sometimes arises for others; either because no suitable balanced incomplete block design exists, or because, for example, it is necessary to make some comparisons more precisely than others. We can see balanced incomplete block designs …