Bayesian Estimation of the Parameter of Rayleigh Distribution under the Extended Jeffrey’s Prior

Abstract

In this paper, Bayes estimators of Rayleigh parameter and its associated risk based on extended Jeffrey's prior under the  assumptions of both symmetric loss function (squared error loss) and asymmetric (precautionary and general entropy ) loss function have been derived. We also derive the highest posterior density (HPD) and equal-tail prediction intervals for the parameter as well as the HPD prediction intervals for future observation.
Monte Carlo simulations are performed to compare the performances of the Bayes estimates under different situations. Finally, An illustrative example is presented to assess how the Rayleigh  distribution fits a real data set.