PREFERENCE OF BAYESIAN METHODS OVER CLASSICAL METHOD IN ESTIMATING THE SCALE PARAMETER OF INVERSE RAYLEIGH FRECHET DISTRIBUTION

Abstract

Among the methods of parameter estimation, maximum likelihood approach is the most often used. However, Maximum likelihood function (MLE) is data dependence, and insufficiecncy of data may cause the results obtained from this method to be unreliable. In this case, the Bayesian method, which allows the usage of the prior knowledge on the parameters in the estimation process, is adopted. This research paper aims to study the Bayesian analysis and
compared it with maximum likelihood estimator on the scale parameter estimation of Inverse Rayleigh Frechet distribution based on uniform and quasi priors and applied Mean square error MSE criteria as a basis for comparison. In the Bayesian method, the Bayes estimates were obtained under Squared Error Loss Function (SELF), Quadratic Loss Function (QLF) and the Precautionary Loss Function (PLF). The performances of these estimators were compared to
the Maximum Likelihood Estimates based on simulation study. The results of this analytic simulation show that the quadratic loss function is the preferred estimators since its posseses the lowest mean Square Error (MSE) under uniform prior and quasi prior. Finally, the results show that quadratic loss functions under Uniform prior and Quasi prior outperformed the squared error loss function, the precautionary loss function and Maximum Likelihood estimator
across different sample sizes.