Two-Component Mixture of Transmuted Fréchet Distribution: Bayesian Estimation and Application in Reliability

Abstract

Transmuted distributions are skewed family of distributions and used to model and analyze reliability data. In this article, Bayesian estimation of the two-component mixture of transmuted Frechet distribution assuming type-I right censored sampling scheme is discussed. In order to estimate the unknown parameters, we consider non-informative and informative priors under squared error loss function, precautionary loss function and quadratic loss function, respectively. Furthermore, Bayesian credible intervals of the model are also discussed. Since the posterior distribution is not in close form, we present a Markov Chain Monte Carlo (MCMC) algorithm to obtain different posterior summaries, including Bayes estimates, posterior risks and credible intervals. The performance of Bayes estimators under different loss functions has been compared in terms of their respective posterior risks by analyzing the simulated and real-life data sets in terms of different sample sizes and censoring rates. Two reliability data sets are also analyzed in this study. Significance In life testing experiments, including prior information related to the phenomenon under investigation helps us in making prediction. To save time and cost, we have utilized the concept of type-I censoring and derived the Bayes estimators and posterior risks of the mixture of Transmuted Frechet distribution. Using simulated and reliability data sets, a comparison assuming different types of priors and loss functions is also given in this study. The choice of transmuted distribution is done on the basis of its flexibility to model skewed data. To compute the Bayes estimates, we have used a MCMC technique.