Bayesian Estimation of Inverse Rayleigh Distribution using Truncated Inverted Gamma as a Prior with different Loss Functions

Abstract

We introduce the truncated prior in Bayesian analysis to refine the posterior distribution and get improved results. The parameter of Inverse Rayleigh (IR) distribution is estimated through Bayesian approach using various loss functions such as squared error loss function, entropy, general entropy, precautionary and squared log error loss function. Two types of Bayes estimators of the posterior expected risks for each loss function i.e. the truncated prior with the proper sampling distribution and the prior as a proper pdf with truncated sampling distribution are studied. In addition, the equal-tail credible intervals are constructed for all the cases. The simulation study is conducted to compare the different Bayes estimators along with the different procedures to seek the best estimators. A real life example is also presented to support the performance of the proposed technique.