Complementary competing risks for bivariate generalized Rayleigh distribution under maximum ranked set sampling

Abstract In this article, inference for a competing risk model is discussed when the cause of failures of units is dependent on using the maximum ranked set sampling (MaxRSS) approach. When the latent failure times follow the bivariate generalized Rayleigh distributions, inference for unknown parameters is obtained using frequentist and Bayesian approaches. Maximum likelihood estimators of the unknown parameter and its existence and uniqueness are also provided. Subsequently, approximate confidence intervals have also been constructed based on the observed Fisher information matrix. In competing risk, it is obvious that one risk is at a higher risk than the other, the MLE of the parameter has been discussed under re-parameterization of the parameter. Further, Bayes estimates have been discussed using informative and non-informative (Jeffrey's and reference) prior under the squared error loss function. Moreover, the associated highest posterior density credible interval is also developed. The performance of various estimators is evaluated based on extensive simulation study, and comments are obtained. Finally, two different real-life applications are also provided for illustrative purposes.