Abstract
Random censoring is an important kind of right censoring in lifetime data analysis. The Rayleigh distributed survival time with a Rayleigh distributed censor time is considered to derive the Maximum Likelihood and the Bayes estimators for the unknown parameters and their corresponding variances. The Uniform and the Square Root Inverted Gamma priors are assumed to find the Bayes estimators under the squared error loss function. The posterior predictive distribution of the future observation, the predictive intervals, the credible intervals and the highest posterior intervals are derived and evaluated. The Inverse transform method of simulation is used to generate data so that the performance of the derived point and interval estimators can be described in terms of numbers. The study is performed for different sample sizes ranging from small to large for various combinations of parameters covering the parameter space to explore and compare properties of the said estimators.