Abstract
This article considers generalized maximum likelihood and Bayesian estimations of reliability parameters under some balanced loss functions when the data are progressively Type II censored from a compound Rayleigh distribution. This is done with respect to a conjugate prior on scale parameter and a discrete prior on shape parameter of the distribution. Posterior risks of generalized maximum likelihood and Bayes estimates are also obtained under balanced loss functions. A real life application to the survival times of patients is also described for the developed estimation methods. A Monte Carlo simulation study has been carried out to examine and compare the performance of estimates on the basis of posterior risks. The simulation study indicates that Bayesian estimation should be preferred over generalized maximum likelihood estimation for estimation of the said parameters. This study will be very useful to researchers, practitioners, and statisticians where such type of life test is needed and especially where a compound Rayleigh model is used.