Efficiency of Bayesian Estimator of Shrinkage by Weighted Loss and Exponential Linear functions for Frecht`s Distribution by Using the Simulation Method

Hayder Sami  Alwan; Safa Najah Abdul  Ameer; Shaymaa Mahood  Mohammed; Maan Abood  Ali

Authors

Hayder Sami Alwan Faculty of Management and Economics, Misan University
Safa Najah Abdul Ameer Faculty of Management and Economics, Misan University
Shaymaa Mahood Mohammed Faculty of Management and Economics, Misan University
Maan Abood Ali Faculty of Management and Economics, Misan University

Keywords:

Frecht`s Distribution, Bayes' Theorem, Probability Density Function, Weighed Loss Function, Linear Exponential Loss Function, Accumulative Density Function, shrinkage estimator

Abstract

This work deals with study of Bayesian shrinkage for parameters of the Frecht`s distribution by following two kinds of loss functions. These are weighted loss function and linear exponential loss function. The simulation method is depended as main manner using the Stata17 program to evaluate the efficiency of the estimators and to find the best Bayesian shrinkage estimator. Bayesian estimators have been derived and then both estimators were calculated by using standardized performance measures to make multi-condition simulation data including six different paths for feasible simulation. Each path checks a different aspect for an effect of sample size and calculates the estimators of the weighted and linear exponential loss functions. After that, a comparison between them is made aiming the arrival to a best estimator.

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