Estimation of parameters of the Mcdonald generalized beta - binomial distribution using estimating functions

Abstract

Recently, there has been a considerable attention on modeling over dispersed binomial data that occur in toxicology, biology, clinical medicine, epidemiology and other related fields using a class of Binomial mixture distribution. Specifically, Beta-Binomial (BB) and Kumaras wamy Binomial distribution (KB) in this class have been extensively used to model the over dispersed Binomial outcomes. A new three parameter binomial mixture distribution namely, McDonald Generalized Beta-Binomial (McGBB) distribution which is superior to KB and BB has been developed. The study on Point estimation for McGBB distribution model has been done using Maximum Likelihood estimates (MLEs) and shown to give better fit than the KB and BB distribution on both real life data set and on the extended simulation study in handling over dispersed binomial data. However, MLEs are quite intensive in computation and not robust to variance misspecification. Estimating functions have for sometimes now been a key concept and subject of inquiry in research as a more general method of estimation which are robust to variance misspecification. This thesis considered estimation of parameters of the McGBB model using Estimating Functions based on Quasi-likelihood (QL) and Quadratic estimating equations (QEEs), which have not been developed and both of which are robust to variance structure misspecification. By varying the coefficients of the QEE’s, four sets of estimating equations, denoted as GL, M1, M2 and M3, were obtained. This study then compared the small sample relative efficiency of the four sets of estimates obtained by the QEE’s and the QL estimates with the MLEs based on a real life data sets arising from alcohol consumption practices and a simulated data. These comparisons show that estimates, using optimal QEEs and estimates of QL are highly efficient and are the best among all estimates investigated. Thus, this thesis has provided an estimation procedure based on the QL and QEEs for estimating the parameters of McGBB distribution which is superior to the Maximum likelihood method