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

Abstract

Abstract The Weibull probability distribution is known to model data from many application areas such as health science, biological science, engineering, finance, economy and education. There is literature on its extension to Beta-Weibull distribution with maximum likelihood estimation of parameters in the model. The Bayesian parameter estimation method is not yet available. In this study, we develop a Bayesian inference for the parameters of the Beta-Weibull distribution, denoted as Bayesian Beta-Weibull distribution. The Bayesian approach defines posterior density with gamma or uniform prior density function. Markov Chain Monte Carlo simulations of the posterior model are conducted in the Stan R package, which is the probabilistic programming language. The results show that the parameters of the Bayesian Beta-Weibull distribution are estimated effectively and the model demonstrates a good fit to simulated data, and real-world datasets. Four real datasets on cancer and under-nutrition status of children are studied. The findings show that the Bayesian method defined for estimation of parameters of Beta-Weibull distribution is a good alternative to the respective maximum likelihood method. Moreover, the method allows integration of available prior knowledge about the parameters and provides robust framework for statistical inference with comprehensive way to assess uncertainty.

Keywords

• Bayesian
• Beta-Weibull distribution
• Inference
• Prior distribution
• Posterior distribution
• Stan