Date of Award
8-2024
Degree Type
Thesis
Degree Name
Master of Science - Statistics
Department
Mathematics and Statistics
First Advisor
Jacob Turner, Ph.D.
Second Advisor
Robert Henderson, Ph.D.
Third Advisor
Jonathan Mitchell, Ph.D.
Fourth Advisor
Jeremy Becnel, Ph.D.
Abstract
The beta distribution is used in numerous real-world applications, including areas such as manufacturing (quality control) and analyzing patient outcomes in health care. It also plays a key role in statistical theory, including multivariate analysis of variance (MANOVA) and Bayesian statistics. It is a flexible distribution that can account for many different characteristics of real data. To our surprise, there has been very little work or discussion on performing statistical hypothesis testing for the mean when it is reasonable to assume that the population is beta distributed. Many analysts conduct traditional analyses using a t-test or nonparametric approach, try transformations, or use standard maximum likelihood-based approaches. We showed via simulations that these tools cannot appropriately control type I error rates for various situations. Additionally, this research has set out to construct a uniformly most powerful test using saddle point approximations. These approximations tend to have better accuracy than traditional likelihood-based methods, even when sample sizes are quite low. We provide the necessary methodology development to perform the test. Further simulation studies on power of test are conducted to compare our new method to traditional approaches and illustrate the superiority of our test in many situations. We also provided recommendations on the best way to use this new approach.
Repository Citation
Kyei, Richard Ntiamoah, "A UNIFORMLY MOST POWERFUL TEST FOR THE MEAN OF A BETA DISTRIBUTION" (2024). Electronic Theses and Dissertations. 565.
https://scholarworks.sfasu.edu/etds/565
Creative Commons License
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Included in
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