Candidate: Beatrice Gathongo,
Title: FINITE AND CONTINUOUS ERLANG MIXTURES WITH THEIR PROPERTIES AND APPLICATIONS
The aim of the proposed research is to construct finite and continuous Erlang mixtures. The finite Erlang mixtures and other distributions such as exponential, gamma, Pareto, among others, will be used as mixing distributions in constructing continuous Erlang mixtures. Continuous Erlang mixtures will also be linked to continuous Poisson and exponential mixtures. Properties of the mixtures will be studied via Moment Generating Functions, moments and mean residual lifetimes. In parameter estimation the following methods will be used: Method of Moments, Maximum Likelihood Estimation, Expectation-Maximization
(EM) Algorithm and Bayesian Estimation. Selected derived mixtures will be fitted to data sets and test their goodness of fit.