Expected total test time and Bayesian estimation for generalized Lindley distribution under progressively Type-II censored sample where removals follow the Beta-binomial probability law

In this paper, we have proposed the progressive Type-II censoring scheme which allows the removals of the live units from a life-test with Beta-binomial probability law during the execution of the experiment. To stablish the theory, the generalized Lindley distribution is considered. For our proposed procedure, the behaviour of the expected total test time has been investigated through the numerical study. The classical as well as the Bayesian procedures for the estimation of the unknown model parameters have also been developed under this censoring scheme. Further, the discussion has been extended to the prediction of the future samples under Bayesian paradigm. Finally, a real data set has been analysed to illustrate the discussed methodology.