Inference and optimal censoring scheme for progressively Type-II censored competing risks model for generalized Rayleigh distribution

This paper considers the statistical inference for the competing risks model from generalized Rayleigh distribution based on progressive Type-II censoring when the parameters of the latent lifetime distributions are different or common. Maximum likelihood estimates are obtained, where the existence of the point estimators are proved, and the confidence intervals are established via the observed Fisher information matrix as well. Bayesian estimates of unknown parameters and reliability characteristics are derived under symmetric and asymmetric loss functions, and Monte Carlo Markov Chain sampling method is used to compute the Bayesian point estimates and the highest posterior density credible intervals. In addition, Bootstrap methods are also considered to obtain bias-corrected point estimates and approximate confidence intervals. Then we carry out hypothesis test using likelihood ratio test statistics. Monte Carlo simulation and a set of real data are presented to assess the performance of our proposed methods. Finally, the optimal censoring scheme issue is studied.