BAYESIAN ESTIMATION OF THE PARAMETERS OF THE WEIBULL DISTRIBUTION UNDER DIFFERENT LOSS FUNCTION USING LINDLEY APPROXIMATION

ABSTRACT

In this study, Bayesian estimators of the parameter of the Weibull distribution is carried out under the linear exponential (LINEX) loss function and generalized entropy loss function (GELF) using the Gamma conjugate prior for the shape parameter and the Jeffreys’ non-informative prior for the scale parameter. The posterior distribution for the estimation of Weibull parameters,  and  are not in closed form. Hence, the Lindley approximation method is used to obtain the Bayesian estimate under the two loss function.

Monte Carlo simulation is used to compare the frequentist maximum likelihood estimator (MLE) with its Bayesian counterpart for the scale and shape parameter of the Weibull distribution through average bias and mean square error of the estimators.

The simulation result shows that the non-classical Bayesian estimates are better than the classical MLE. It is also observed that the Bayesian estimator under the LINEX loss function has the smallest value of MSE in all cases, which makes it the best estimator for both the shape and scale parameters of the Weibull distribution.