A study the effect of the loss functions on E-Bayesian estimation and
E-MSE for reliability parameters
Abstract
In order to measure the estimated error, the definition of
E-MSE(expected mean squared error) is introduced based on the definition
of E-Bayesian estimation. Moreover, under different loss
functions(include: squared error loss, K-loss function, precautionary
loss and entropy loss), the formulas of E-Bayesian estimation and E-MSE
for reliability parameters of exponential distribution are given
respectively. Monte Carlo simulations are performed to compare the
performances of the proposed methods of estimation and a real data set
have been analysed for illustrative purposes(also using OpenBUGS),
results are compared on the basis of E-MSE. When considering evaluating
the E-Bayesian estimations under different loss functions, this paper
proposed the E-MSE as evaluation standard.