One- and two-sample prediction for the progressively censored Rayleigh residual data

In this work, we consider the problem of estimating the scale and location parameters and predicting the unobserved or removed data based on the Rayleigh progressive type II censored residual sample. First, we consider the classical and Bayesian methods to estimate and also to construct confidence and credible intervals of the scale and location parameters. Second, we consider one- and two-sample Bayesian prediction of the removed ordered data based on some observed data. The Monte Carlo and Metropolis-Hastings algorithms are used to compute simulation point predictors and prediction intervals for the removed units in multiple stages of the censored sample. Numerical comparisons on artificial and real-life data are conducted to assess the performance of the estimators of the parameters, as well as the predictors of missing and future ordered data, using some intensive computer programs.