Cure fraction models are usually meant for survival data that contains a proportion of non-subject individuals for the event under study. In order to get an accurate estimate of the cure fraction model, researchers often used one of two models: the mixture model or the non-mixture model. This study presents both mixture and non-mixed cure fraction models, together with a survival data format that is based on the beta-Weibull distribution. In this body of work, an alternative extension to the Weibull distribution was devised for the purpose of analyzing lifetime data. The beta-Weibull distribution is a four-parameter distribution established in this study as an alternate extension to the Weibull distribution in lifetime data analysis. The suggested addition allows for the inclusion of covariate analysis in the model, with parameter estimation performed using a Bayesian approach and Gibbs sampling methods. In addition, a simulation study was carried out to emphasize the benefits of the new development.
