Estimation of P(Y < X) for modified Weibull distribution under progressive Type-II censoring

In this study, we consider the estimation of R = P(Y < X) under progressive Type-II censoring scheme when X and Y are independent modified Weibull distributed random variables with different scale but same shape and accelerated parameters. The estimation of R is carried out both in case of known and unknown shape and accelerated parameters. For unknown model parameters, we derive maximum likelihood and Bayes estimators of R. In Bayesian estimation, we use importance sampling and Markov Chain Monte Carlo techniques to obtain Bayes estimate of R. Further, for known model parameters, we determine exact sampling distribution of the maximum likelihood estimator of R, and hence exact confidence interval for R is constructed. The uniformly minimum variance unbiased estimator and Lindley approximate Bayes estimator of R have also been derived. A simulation study is performed to compare different proposed methods of estimation. Finally, for illustration, a real-data analysis is provided.