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

Abstract

Transmuted distributions are skewed distributions and recently attracted a great attention of researchers due to their applications in reliability and statistics. In this article, our main focus is on the Bayesian estimation of two-component mixture of the 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) are also constructed. A 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, comparison of these Bayes estimators is 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 patients while 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.

On Estimation of Three-Component Mixture of Distributions via Bayesian and Classical Approaches

“…Probability density function of n th order statistic: substituting k � n in (21) and after little algebraic simplification, the pdf of n th order statistic is…”

“…For a detailed appraisal of classical techniques for estimation and applications of mixture distributions, we refer to studies by Sultan et al [7], Abu-Zinadah [8], and Kamaruzzaman et al [9] among others. On the other hand, the estimation of parameters in Bayesian framework for a mixture of two distributions has been considered by many researchers [10][11][12][13][14][15][16][17][18][19][20][21]. Contrary to the two-component mixture modeling, some authors have discussed situations where data are assumed to follow a three-component mixture of suitable probability distributions [22][23][24][25][26][27][28].…”

Monitoring Lifetime Data for a Failure Censoring Reliability Test with Replacement Using Shewhart Type and Exponentially Weighted Moving Average Control Charts

“…X-bar control chart is proposed in 16 to monitor the inverse Rayleigh distribution while repetitive group sampling is employed. Reference 17 provides Bayesian estimations for a transformed Weibull distribution under type I right censoring. In the following, Table 1 summarizes some of the research in the scope of the current study.…”