Physical Sciences and Mathematics Commons^™

Bayesian Inference For Decision Making, Ming-Yih Kao

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

In recent years, Bayesian inference has become very popular in applied statistics. This study will present the fundamental concept of Bayesian inference and the basic techniques of application to statistical quality control, marketing research, and other related fields.

Stochastic Processes Model And Its Application In Operations Research, Chun Yuan Hsu

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

Just as the probability theory is regarded as the study of mathematical models of random phenomena, the theory of stochastic processes plays an important role in the investigation of random phenomena depending on time. A random phenomenon that arises through a process which is developing in time and controlled by some probability law is called a stochastic process. Thus, stochastic processes can be referred to as the dynamic part of the probability theory. We will now give a formal definition of a stochastic process.

Let T be a set which is called the index set (thought of as time), then, …

Computer Programs For Incomplete Block Designs, Fred Miller

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

In most disciplines where research is involved, there exists an occasional problem of having minimal facilities and/or funds for conducting experiments. This often necessitates the use of designs known as incomplete block designs.

Since the calculations needed to provide an appropriate statistical analysis are somewhat tedious, particularJ..y in the larger designs, it is advantageous to have computer programs to do the necessary calculations.

There are several computer programs at Utah State University written in Fortran II language with Forcom subroutines that perform the analyses for incomplete block designs. These programs, for the most part, were authored by Justus Seely and …

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 …

A Study Of The Exponential Distirbutions And Their Applications, Michael Chang-Yu Wang

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

The exponential distribution is a widely known distribution i n statistical theory. It can be regarded as the continuous analogue of the Poisson distribution, discussed by S. D. Poisson in 1837. The Poisson is a limiting form of the Binomial distribution which can be t race d back as early as 1700, discussed by James Bernoulli. A paper by Marsden and Barratt (1911) on the radioactive disintegration of thorium gives a typical frequency distribution which follows the exponential law (8, p. 89). The exponential distribution has achieved importance recently in connection with the theory of stochastic process and has found …

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 …