Comparison of Bayes' Estimators for the Exponential Reliability Function Under Different Prior  Functions

Abbas Naser Al-obedy, Jinan

	Comparison of Bayes' Estimators for the Exponential Reliability Function Under Different Prior Functions
Ibn Al-Haitham Journal For Pure And Applied Science
Article 1, Volume 30, Issue 1, 2017, Pages 208-236
Author
Jinan Abbas Naser Al-obedy
Abstract
In this study, we derived the estimation for Reliability of the Exponential distribution based on the Bayesian approach. In the Bayesian approach, the parameter of the Exponential distribution is assumed to be random variable .We derived posterior distribution the parameter of the Exponential distribution under four types priors distributions for the scale parameter of the Exponential distribution is: Inverse Chi-square distribution, Inverted Gamma distribution, improper distribution, Non-informative distribution. And the estimators for Reliability is obtained using the two proposed loss function in this study which is based on the natural logarithm for Reliability function .We used simulation technique, to compare the resultant estimators in terms of their mean squared errors (MSE).Several cases assumed for the parameter of the exponential distribution for data generating of different samples sizes (small, medium, and large). The results were obtained by using simulation technique, Programs written using MATLAB-R2008a program were used. In general, we obtained a good estimations of reliability of the Exponential distribution under the second proposed loss function according to the smallest values of mean squared errors (MSE) for all samples sizes (n) comparative to the estimated values for MSE under the first proposed loss function
Keywords
The Exponential; Bayes method; the prior distributions; square distribution; Inverted Gamma distribution; improper distribution; non; informative distribution; mean squared errors; Improper; non; informative; MSE

Statistics Article View: 137 PDF Download: 102