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Abstract:In this study, we consider statistical inference problems for the residual life data that come from the Rayleigh model based on type II censored data. Maximum likelihood and Bayesian approaches are used to estimate the scale and location parameters for the Rayleigh model, the Gibbs sampling procedure is used to draw Markov Chain Monte Carlo (MCMC) samples and MCMC samples have been used to compute the Bayes estimates and to construct symmetric credible intervals. Furthermore, we estimate the posterior predictive density of the future ordered data and then obtain the corresponding predictors. The Gibbs and Metropolis samplers are used to predict the life lengths of the missing lifetimes in multiple stages of the residual type II censored sample. Numerical comparisons for a real life data involving the ball bearings' lifetimes and the artificial data are conducted to assess the performance of the parameters' estimators and the predictors of future ordered data using some specialized computer programs.

Based on a record sample from the Rayleigh model, we consider the problem of estimating the scale and location parameters of the model and predicting the future unobserved record data. Maximum likelihood and Bayesian approaches under different loss functions are used to estimate the model's parameters. The Gibbs sampler and Metropolis-Hastings methods are used within the Bayesian procedures to draw the Markov Chain Monte Carlo (MCMC) samples, used in turn to compute the Bayes estimator and the point predictors of the future record data. Monte Carlo simulations are performed to study the behaviour and to compare methods obtained in this way. Two examples of real data have been analyzed to illustrate the procedures developed here.