A BAYESIAN APPROACH TO ESTIMATE THE PARAMETERS OF WEIBULL SURVIVAL DISTRIBUTION

vii ABSTRACT This research has implemented a Bayesian estimation procedure for the Weibull survival distribution without covariates.Weibull survival distribution is a two-parameter distribution,and is just one out of several survival distributions used for tackling problems in survival analysis which may be classified under an uncensored or censored case(with or without covariates).As the review of literature unraveled the absence of a good number of literature addressing the need for an alternative procedure which considers these peculiar cases for a Weibull survival distribution,the aim of this study was to look in this direction with strict focus placed on the uncensored case.Hence,the Bayesian estimation procedure was employed to estimate the parameters of the Weibull survival distribution,and to deduce the survivorship function.The process of implementing this routine gave rise to a theorem and an axiom having an accompanying proof and deduction respectively provided. Estimates of the Weibull parameters obtained using the Bayesian estimation procedure in this study showed divergence from those obtained using maximum likelihood estimation procedure,with the procedure for estimating the said parameters via maximum likelihood estimation being more complex than that of the Bayesian estimation procedure.The comparative analysis performed by the simulation of procedures for the MLE and Bayesiar estimation techniques have shown marked divergence between the estimates of the scalk parameter λ.This divergence may be as a result of imprecision of the gamma distributior as the right prior.