Estimation and Prediction for General Progressive Censored Rayleigh Model

This paper describes Bayesian and non-Bayesian inference and prediction of the Rayleigh distribution for general progressively Type-II censored data. First we consider the maximum likelihood and the Bayesian inference of the unknown parameter, reliability function and hazard rate function. This was done under symmetric (squared error loss function), and asymmetric loss functions (linear exponential and general entropy loss functions). We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We further consider two-sample Bayes prediction problem based on general progressive censored sample as a past sample. A study of 10000 randomly future observations shows that the actual prediction level is satisfactory. A real data representing the survival times of a group of lung cancer patients is used to illustrate all the results developed here.