On the joint Type-II progressive censoring scheme

Recently the progressive censoring scheme has been extended for two or more populations. In this article we consider the joint Type-II progressive censoring (JPC) scheme for two populations when the lifetime distributions of the experimental units of the two populations follow two-parameter generalized exponential distributions with the same scale parameter but different shape parameters. The maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms. We propose to use the expectation maximization (EM) algorithm to compute the maximum likelihood estimators. The observed information matrix based on missing value principles is derived. We study the Bayesian inference of the unknown parameters based on a beta-gamma prior for the shape parameters, and an independent gamma prior for the common scale parameter. The Bayes estimators with respect to the squared error loss function cannot be obtained in explicit form. We propose to use the importance sampling technique to compute the Bayes estimates and the associated credible intervals of the unknown parameters. Extensive simulation experiments have been performed to study the performances of the different methods. Finally a real data set has been analyzed for illustrative purposes.