On the Bayesian Analysis of Two-Component Mixture of Transmuted Weibull Distribution

Document Type: Article

Authors

1 Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan.

2 Department of Statistics, Quaid-i-Azam University

3 Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan

Abstract

Transmuted distributions are skewed distributions and recently attracted a great attention of researchers due totheir applications in reliability and statistics. In this article, our main focus is on the Bayesian estimation of two-component mixture of Transmuted Weibull Distribution (TWD) under 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) were also constructed. Markov Chain Monte Carlo (MCMC) technique is adopted to generate samples from the posterior distributions and in turn computing different posterior summaries including Bayes estimates(BEs), posterior risks(PRs) and Bayesian credible intervals (BCI). As an illustration comparision of these Bayes estimators are made through simulated under different loss functions in terms of their respective posterior risks assuming different sample sizes and censoring rates. Two real-life examples; the first being the survival times of hepatitis B & C patientswhile the second being the hole diameter of 12 mm and the sheet thickness is 3.15 mm are also discussed to illustrate the potential application of the proposed methodology.

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