Bayesian Estimation of Exponentiated Rayleigh Distribution under Symmetric and Asymmetric Loss Functions

In this paper, we have considered the estimation problem of one-parameter exponentiated Rayleigh distribution. The parameters are estimated using likelihood based inferential procedure. We have computed MLEs and Bayes estimates under informative and non-informative priors along with six different loss functions, the Bayes estimation was obtained “Squared error, Linear exponential, Precautionary, Entropy, De Groot and non-Linear exponential loss functions”. Finding a good estimator of the unidentified shape parameter is the study's main goal. The Bayesian estimates of the parameter of exponentiated Rayleigh distribution are obtained using Markov chain Monte Carlo (MCMC) simulation method. All the computations are performed in OpenBUGS and R software.