Electronic Theses and Dissertations



Document Type


Degree Name

Doctor of Philosophy


Mathematical Sciences

Committee Chair

Dale Bowman

Committee Member

Ebenezer George

Committee Member

Lih-Yuan Deng

Committee Member

Ching-Chi Yang


In the statistical analysis of binary data, usually the binomial distribution is themost commonly used probability model in many applications. The binomial is a very usefuldistribution in many practical applications due to its simplicity and having a parameter thathas an intuitive meaning. However, it has a unique feature that is the variance depending onthe mean, an assumption that does not reflect reality in many practical applications especiallyin cases where the data exhibits greater variability than predicted by the distribution. Thetwo-parameter double binomial model introduced by Efron (1986) may be considered as auseful alternative to the one-parameter binomial distributions, given that it can account forboth overdispersion and underdispersion. In this dissertation, we obtain maximum likelihoodestimates for the double binomial distributions. The Bayesian methodology is also consideredfor estimation procedures and we demonstrate that, under the model assumptions, the fullyconditional posterior distributions that are obtained allow for the estimation of posteriordistributions via the Gibbs sampling algorithm. A toxicity data set involving the effect ofethylene glycol in mice is analyzed using our considered methodology.


Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to ProQuest