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The generalized progressive hybrid censoring schemes (GPHCS) have become quite popular in the case when there are very few failures before pre-determined time  T  in progressive hybrid censoring schemes. Whereas the GPHCS always ensures a fixed number of failures, which makes this scheme very popular. In this paper, we introduce a new joint generalized progressive hybrid censoring scheme (J-GPHCS) for two independent samples from different populations. We place both the samples simultaneously on the life testing experiment. Further, we assume the lifetime of the experimental units, under both samples, to follow exponential distribution with meanand, respectively. The maximum likelihood estimators, of the unknown parameters and their exact distributions, are derived. Asymptotic and bootstrap confidence intervals are also constructed. Further, the Bayesian inference of some unknown parametric functions is considered under a very flexible Inverse-Gamma priors. We also obtain the Bayes estimators, and associated credible intervals of the unknown parameters. Extensive simulation studies are performed to investigate the proposed estimators. Finally, the methods are illustrated with the analysis of a real data set.

Exact likelihood inference for two exponential populations under jointly generalized progressive hybrid censoring