Statistical inference for the generalized Rayleigh distribution based on upper record values

摘要

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.