Bayesian Estimation under Different Loss Functions Using Gamma Prior for the Case of Exponential Distribution
Keywords:Bayes estimator, Maximum likelihood estimator (MLE), Squared error (SE) loss function, Modified linear exponential (MLINEX) loss function, Non-Linear exponential (NLINEX) loss function.
The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). Since exponential distribution is the life time distribution, we have studied exponential distribution using gamma prior. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. We have used simulated data using R-coding to find out the mean squared error (MSE) of different loss functions and hence found that non-classical estimator is better than classical estimator. Finally, mean square error (MSE) of the estimators of different loss functions are presented graphically.
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