Linear Bayes Estimator For The Parameters Of The Inverse Gaussian Distribution

The inverse Gaussian distribution has many excellent properties,and it is widely used in the life test,management science,actuarial science and other fields.Aiming at the parameters estimation of the inverse Gaussian distribution,many scholars have put forward a lot of estimation methods such as the maximum likelihood estimation,the unbiased estimation,the Bayes estimation and so on.In this paper,we employ the linear Bayes method to estimate the parameters of the inverse Gaussian distribution.The main idea of this method is to estimate the parame-ters using the linear expression of the statistics of the samples.We can obtain the linear Bayes estimator expression based on three statistics X,T and XT,and five statistics X,T,XT,X2 and T2.Under the mean square error matrix criterion,we prove the linear Bayes estimator using five statistics performs better than that of using three statistics.At the same time,we also prove the linear Bayes estimators are superior to the classical maximum likelihood estimation and the unbiased estimation.Normally,it is difficult to obtain the Bayes estimation solution due to the complex-ity of the integral in the calculation process.We often use MCMC method to obtain the Bayes estimator.This article also use Lindley approximation method to obtain the approximation expression of the Bayes estimator under the square loss function.In the case of different prior distributions,we respectively simulate the distance between the linear Bayes estimator using different number of statistics and the Bayes estimator,and the distance between the Lindley approximation and the Bayes estimator as well,the simulation results show that the more number of statistics we use,the better the linear Bayes estimator performs.