Bayesian Inference for the Beta-Weibull Distribution with Applications to Cancer and Under-nutrition Data

Abstract The Weibull probability distribution can be used to model data from many subject areas such as survival data in health, reliability data in engineering and insurance, and life data in biological science. This distribution was further extended to the Beta-Weibull distribution in literature, however, its Bayesian parameter estimation method is not yet available. In this study, we provide a Bayesian inference for the Beta-Weibull distribution, denoted as Bayesian Beta-Weibull distribution. The Bayesian approach with gamma distribution and uniform prior density functions are proposed and studied. Simulations of the Bayesian posterior model are conducted in the Stan R package, which is the probabilistic programming language. The full Bayesian statistical inference is implemented with Markov Chain Monte Carlo simulations. The results show that the parameters of the Bayesian Beta-Weibull distribution are estimated effectively and the model demonstrates a good fit to the simulated data and real-world data sets considered. We conclude from this study that the Bayesian inference for the parameters of Beta-Weibull distribution is found to be more reliable and comparable to the Maximum Likelihood estimation method in data fitting to various health applications, for example, cancer and under-nutrition data sets studied.