Bayesian Analysis for the Generalized Rayleigh Distribution

In this paper, the estimation problem of generalized Rayleigh distribution is considered. The parameters are estimated using likelihood based inferential procedure: classical as well as Bayesian. We have computed MLEs and Bayes estimates under gamma priors along with their asymptotic confidence, bootstrap and HPD intervals. The Bayesian estimates of the parameters of generalized Rayleigh distribution are obtained using Markov chain Monte Carlo (MCMC) simulation method. We have obtained the probability intervals for parameters, hazard and reliability functions. The posterior predictive check method has been applied for evaluating the model fit. We have also discussed the Bayesian estimation and prediction for Type-II censored data. All the computations are performed in OpenBUGS and R software. A real data set is analyzed for illustration of the proposed inferential procedures.