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.

Automated summary

This paper discusses statistical inference for competing risks model using generalized Rayleigh distribution and progressive Type-II censoring, considering different or common parameters for latent lifetime distributions. Maximum likelihood estimates and Bayesian estimates are obtained, while Bootstrap methods and hypothesis testing are also carried out. Performance evaluation is done through Monte Carlo simulation and real data, and optimal censoring scheme issue is addressed.