E-Bayesian and Hierarchical Bayesian Estimations Based on Dual Generalized Order Statistics from the Inverse Weibull Model
Hesham M. Reyad *
College of Business and Economics, Qassim University, Kingdom of Saudi Arabia.
Adil M. Younis
College of Business and Economics, Qassim University, Kingdom of Saudi Arabia.
Soha A. Othman
Institute of Statistical Studies and Research, Cairo University, Egypt.
*Author to whom correspondence should be addressed.
Abstract
This paper is devoted to compare the E-Bayesian and hierarchical Bayesian estimations of the scale parameter corresponding to the inverse Weibull distribution based on dual generalized order statistics. The E-Bayesian and hierarchical Bayesian estimates are obtained under balanced squared error loss function (BSELF), precautionary loss function (PLF), entropy loss function (ELF) and Degroot loss function (DLF). The properties of the E-Bayesian and hierarchical Bayesian estimates are investigated. Comparisons among all estimates are performed in terms of absolute bias (ABias) and mean square error (MSE) via Monte Carlo simulation. Numerical computations showed that E-Bayesian estimates are more efficient than the hierarchical Bayesian estimates.
Keywords: E-Bayesian estimates, inverse Weibull distribution, hierarchical Bayesian estimates, loss functions, Monte Carlo simulation.