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Journal of Probability and Statistics
Volume 2013, Article ID 146140, 16 pages
http://dx.doi.org/10.1155/2013/146140
Research Article

Bayesian Estimation and Prediction for Flexible Weibull Model under Type-II Censoring Scheme

Department of Statistics and DST-CIMS, Banaras Hindu University, Varanasi 221005, India

Received 4 April 2013; Revised 3 June 2013; Accepted 18 June 2013

Academic Editor: Shein-chung Chow

Copyright © 2013 Sanjay Kumar Singh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We have developed the Bayesian estimation procedure for flexible Weibull distribution under Type-II censoring scheme assuming Jeffrey's scale invariant (noninformative) and Gamma (informative) priors for the model parameters. The interval estimation for the model parameters has been performed through normal approximation, bootstrap, and highest posterior density (HPD) procedures. Further, we have also derived the predictive posteriors and the corresponding predictive survival functions for the future observations based on Type-II censored data from the flexible Weibull distribution. Since the predictive posteriors are not in the closed form, we proposed to use the Monte Carlo Markov chain (MCMC) methods to approximate the posteriors of interest. The performance of the Bayes estimators has also been compared with the classical estimators of the model parameters through the Monte Carlo simulation study. A real data set representing the time between failures of secondary reactor pumps has been analysed for illustration purpose.