Bayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss Functions

In this paper, a Bayesian approach is proposed for shift point detection in an inverse Gaussian distribution. In this study, the meanparameter of inverse Gaussian distribution is assumed to be constant and shift points in shape parameter is considered. First the posteriordistribution of shape parameter is obtained. Then the Bayes estimators are derived under a class of priors and using various loss functions.We assumed uniform, Jeffreys, exponential, gamma and chi square distributions as prior distributions. The squared error loss function(SELF), entropy loss function (ELF), linex loss function (LLF) and precautionary loss function (PLF), are used as loss functions. Weattempt to find out the best estimator for shift point under various priors and loss functions. The proposed Bayesian approach can beadapted to any similar problem for shift point detection. Simulation studies were done to investigate the performance of different lossfunctions. The results of simulation study denote that the Jeffrey prior distribution under PLF has the most accurate estimation of shift pointfor sample size of 20, and the gamma prior distribution under SELF has the most accurate estimation of shift point for sample size of 50

کلیدواژه ها:

Bayes estimators ، shift point ، inverse Gaussian distribution ، loss function