Electronic Theses and Dissertations





Document Type


Degree Name

Doctor of Philosophy


Mathematical Sciences



Committee Chair

Ebenezer O. George

Committee Member

Su Chen

Committee Member

Hongmei Zhang

Committee Member

Dale Bowman


This dissertation addresses two types of problems in Applied Statistics. The first deals with the development of a procedure for estimating the correlation structure of RNA-Seq. data and the second type involves introducing a model that can be used to estimate significance of Genesets based on count data such as RNA-Seq. The approach we adopt is to model the RNA-Seq. data by exchangeable negative multinomial distribution. In the first Chapter, we give an overview of the structure of the dissertation, introduce some definition and also introduce the Exchangeable NegativeMultinomial Distribution resulting from relaxing the independence of the Multinomial distribution to exchangeability. It is demonstrated that the proposed model can be characterized by infinitely many parameters that form a completely monotone sequence. In Chapter 3, A weighted least squares algorithm is derived for a special case of the distribution for estimating the parameters for a finite sample. A likelihood ratio test is developed to show the dierence between treatments that follow this distribution. Chapter 4 is dedicated to a simulation study conducted to illustrate the distribution, showing the mean and variance for some select values of p1, p2, p3, and which are parameters of the model. A full likelihood procedure is described which can be used to investigate correlated and overdispersed count data common in bio-medical sciences. In the end, the introduced distribution is applied to analyze a Geneset containing 10 genes and 24 samples for lung cancer patients.


Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.