Affiliations: [a] Department of Statistics, St. Anthony's College, Shillong, Meghalaya, India | [b] Department of Quantitative Health Sciences, Cleveland Clinic, Cleveland, OH, USA | [c] Department of Biostatistics, University of North Carolina at Chapel Hill, NC, USA
Corresponding author: Tanujit Dey, Department of Quantitative Health Sciences, Cleveland Clinic, Cleveland, OH, USA. E-mail:[email protected]
Abstract: We consider the problem of estimating the parameters of generalized Rayleigh distribution both from frequentist and Bayesian point of view when the available data is in the form of record values. Bayes' estimators of the unknown parameters are obtained under symmetric and asymmetric loss functions using gamma priors on both the shape and the scale parameters. The Bayes estimators cannot be obtained in explicit forms. So we propose Markov Chain Monte Carlo (MCMC) techniques to generate samples from the posterior distributions and in turn computing the Bayes estimators. We have also derived the Bayes intervals of the parameters and discussed both frequentist and the Bayesian prediction intervals of the future record values based on the observed record values. Monte Carlo simulations are performed to compare the performances of the proposed methods, and one data set has been analyzed for illustrative purposes.
Keywords: Bayes estimator, Bayes prediction, general entropy loss function, maximum likelihood estimator, median prediction