Estimation of the mean and the reciprocal of the mean of the inverse Gaussian distribution

The uniformly minimum variance unbiased estimator for the reciprocal of the mean of an inverse Gaussian distribution may be negative when the sample size is small and coefficient of variation is large. A class of estimators has been proposed in which the estimators are always positive and have smaller mean squared error than the uniformly minimum variance unbiased estimator. Some estimators for the mean are also proposed which have smaller mean squared error than the usual estimator