On the Bayesian analysis of two-component mixture of transmuted Weibull distribution

Transmuted distributions are skewed distributions that have recently attracted the attention of researchers due to their applications in reliability and statistics. In this article, the main focus is on the Bayesian estimation of a two-component mixture of the Transmuted Weibull Distribution (TWD) under a type-I right censored sampling scheme. In order to estimate the unknown parameters, non-informative and informative priors under Squared Error Loss Function (SELF), Precautionary Loss Function (PLF) and Quadratic Loss Function (QLF) are assumed when computing the posterior estimations. In addition, the Bayesian Credible Intervals (BCI) are also constructed. A Markov Chain Monte Carlo (MCMC) technique is adopted to generate samples from the posterior distributions and, in turn, to compute dierent posterior summaries, including Bayes Estimates (BEs), Posterior Risks (PRs) and BCI. As an illustration, comparison of these Bayes estimators is made through simulation under dierent loss functions in terms of their respective PRs, assuming dierent sample sizes and censoring rates. Two real-life examples, the rst being the survival times of hepatitis B & C patients, while the second being a hole diameter of 12 mm and a sheet thickness of 3.15 mm, are also discussed to illustrate the potential application of the proposed methodology.