Bayesian analysis for the exponentiated Rayleigh distribution

Statistical models such as gamma, Weibull, log-normal and generalized exponential models are extremely important in analyzing lifetime and industrial data. The exponentiated Rayleigh model can be used as an alternative to the gamma and Weibull models for analyzing data. In this article, Bayesian estimation and prediction for the exponentiated Rayleigh model, using informative and non-informative priors, have been considered. An importance sampling technique is used to estimate the parameters, as well as the reliability function. The Gibbs and Metropolis samplers are used to predict the behavior of future observations from the distribution. Two data sets are used to illustrate our procedures.