BAYESIAN ESTIMATION OF THE SHAPE PARAMETER OF GENERALIZED INVERSE EXPONENTIAL DISTRIBUTION UNDER NON-INFORMATIVE PRIORS

Abstract

In this paper, the shape parameter of the Generalized Inverse Exponential Distribution (GIED) was estimated using both maximum likelihood and Bayesian estimation techniques. The Bayes estimates are obtained using squared error loss function and precautionary loss function by considering Uniform prior, Jeffery’s prior and Extended Jeffery’s prior. Thus the study considered these three priors under the square error loss function and also the same three priors under precautionary loss function to derive the estimators for the shape parameter. The estimator with minimum posterior risk and mean square error (MSE) as criteria is selected as the best. To achieve this, an extensive Markov Chain Monte Carlo (MCMC) simulation study was carried out to compare the performances of the Bayes and maximum likelihood estimates at different sample sizes. Based on mean square error (MSE), the results reveal that the Bayes estimates performed better than maximum likelihood estimates. Based on posterior risk, Bayes estimates using Square Error Loss Function under the Extended Jeffery’s Prior (SELFEXJ) performed best among the six non-informative priors considered under different sample sizes. Hence the Bayes estimate under the Extended Jeffrey’s using the squared error loss function has the best estimator for estimating the shape parameter of the model.