Bayesian estimation for Life-Time distribution parameter under Compound Loss Function with Optimal Sample Size Determination

Abstract

Abstract: This research aims to find Bayes estimator under symmetric and asymmetric two loss functions, such as the squared Log error loss function and entropy loss function, as well as a loss function that combines these two functions. It's called compound loss function, which is asymmetric in nature. A comparison of the Bayes estimators for scale parameter of Life-Time distribution, which includes a collection of known distributions under the compound proposed loss function, and its contained loss functions as well as the estimation of optimal sample size. Using a mean square error criterion (MSE), where the generation of the random data using the simulation for estimate Weibull distribution parameters that represents a special case of Life-Time distribution different sample sizes (n=10,50,100) and (N=1000), taking initial values for the parameters , to get to the balanced estimator that add between two loss functions.