Bayes Estimators of the Scale Parameter of an Inverse Weibull Distribution under two different Loss Functions

In this paper we obtain Bayesian estimators of the scale parameter of the inverse Weibull distribution (IWD).We derive those estimators under two different loss functions: the quasisquared error loss function and the nonlinear exponential loss function (NLINEX). Two priors are considered for finding the estimators: a class of natural conjugate informative prior, namely; the exponential prior information and inverted-Levy prior information. Based on a Monte Carlo simulation study, the performance of those estimators is compared. The comparison criteria, the mean square errors (MSE) are computed and presented in tables. Comparison results show that MLE was the best followed by Bayes estimators based on the inverse Levy prior under NLINEX loss function which was preferable among the others

Comparison of Maximum Likelihood and some Bayes Estimators for Maxwell Distribution based on Non-informative Priors

In this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of Bayes estimators of the shape parameter of the Maxwell distribution decreases with the increase of Jeffreys prior constants. The results also show that values of Bayes estimators are almost close to the maximum likelihood estimator when the Jeffreys prior constants are small, yet they are identical in some certain cases. Comparison with respect to loss functions show that Bayes estimators under the modified squared error loss function has greater MSE than the squared error loss function especially with the increase of r