Bayesian estimation and prediction based on Rayleigh record data with applications

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.