Term of Award

Spring 2021

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


Department of Mathematical Sciences

Committee Chair

Stephen Carden

Committee Member 1

Arpita Chatterjee

Committee Member 2

Divine Wanduku


This thesis project will analyze the bias in mixture models when contaminated data is present. Specifically, we will analyze the relationship between the bias and the mixing proportion, p, for the rank correlation methods Spearman’s Rho and Kendall’s Tau. We will first look at the history of the two non-parametric rank correlation methods and the sample and population definitions will be introduced. Copulas will be introduced to show a few ways we can define these correlation methods. After that, mixture models will be defined and the main theorem will be stated and proved. As an example, we will apply this theorem to the Marshall-Olkin distribution. This will allow us to show the bias graphically for each of the different correlation methods.

OCLC Number


Research Data and Supplementary Material