A Note on Bayesian Analysis of Error Function Distribution under Different Loss Functions

The Bayesian analysis of the scale parameter of error function distribution has been considered in this paper. A class of informative and non-informative priors has been assumed to derive the corresponding posterior distributions. The Bayes estimators and associated risks have calculated under different loss functions. The Bayesian credible intervals have been constructed under each prior. The performance of the Bayes estimators have been evaluated and compared under a comprehensive simulation study. The purpose is to find out the combination of a loss function and a prior having the minimum Bayes risk and hence producing the best results. The study depicts that in order to estimate the said parameter use of entropy loss function under informative priors can be preferred.