Bayesian Estimation of The unknown parameter of Inverse Rayleigh Distribution (IRD) based on GELF

Abstract

In this paper, we investigated the Bayesian estimation of the unknown parameter of the Inverse Rayleigh Distribution (IRD) under different priors, represented by the inverse gamma distribution, the inverse chi-squared distribution, and the standard Levy distribution as priors. We obtained the posterior distributions for the unknown parameter of IRD under the different priors based on the general entropy loss function (GELF). We assumed different values for the shape parameter of GELF. Also, the maximum likelihood estimator (MLE) is used to estimate the scale parameter of IRD. Then, a study is conducted to obtain the results, based on the different parameters of Inverse Rayleigh distribution and sample sizes. We found that Bayes estimators perform better than MLE according to the least mean square error (MSE) Criterion

Keywords

• The inverse Rayleigh distribution, MLE, Bayes estimation, GELF, MSE