The Shape Parameter Estimator Of Inverse Gauss Distribution Under The Q-Symmetric Entropy Loss

The symmetric loss function is of great importance in the theory of statistical decision, such as squared loss function, which refleCtS the fact that if an action is close to, then the decision is reasonable and little loss is incurred. If is far from, then a large loss is incurred and therefore is not good. In fact, the admissibility of the estimator may depend quite sensitively on features of the loss function. So it is important to do more study of the properties of alternative estimators relative to other types of symmetric loss function. This paper deals with Bayes estimator for the shape parameter of inverse Gauss distribution when the mean parameter is known under the q- symmetric entropy joss, and discusses the admissibility and inadmissbility of estimator with the form of (cT+d)^-1.The first part of the article give a brief introduction of inverse Gauss distribution; The second part of the article give a brief account of the back ground of the theory of statistical decision and Bayes decision, the concept of admissibility and inadmissibility, and so on. Part three deals with Bayes estimator for the shape parameter of inverse Gauss distribution when the mean parameter is known under the q- symmetric entropy joss, and discusses the admissibility and inadmissbility of estimator with the form of (cT + d)^-1. Conclusion of this work is done to conclude the estimation method, moreover we discuss the feasibility and what we have to improve and explored in deep research.