A Bayesian Parametric Estimation of Beta Kumaraswamy Burr Type X (Beta Kum-BX) Distribution Based on Cure Models with Covariates

Abstract

In statistical models for censored survival data which includes a proportion of individuals who are not subject to the event of interest under study are known as the long-term survival cured models. It has two most adopted and common models used in estimating the cure fraction namely: the mixture (standard cure) and the non-mixture models. In this research work, we introduce a Bayesian approach using the two models for survival data based on the Beta Kumaraswamy Burr Type X distribution with six parameters and compared with two existing models: beta-Weibull and beta-generalized exponential distributions in analyzing a real-life dataset. The proposed approach allows the inclusion of covariates in the model. The parameter estimation was obtained by maximum likelihood and Bayesian analysis methods. The win Bugs and MCMC pack library in R softwares were employed for the Gibbs sampling algorithm in other to obtain the posterior summaries of interest and also the trace plots by the applying of real data sets and a simulation study was done based on cure models to compare the performance of both models relating to actual sense of motivation and novelty which clarifies the usefulness of the proposed methodologies.