On the efficiency of a testimator for the mean of an inverse Gaussian distribution

Though the sample mean is a natural estimator for the mean [mu] of an Inverse Gaussian (IG) distribution having another parameter [lambda], when a guess [mu]0 for [mu] seems plausible, an alternative adaptive estimator which shrinks towards [mu]0 when a preliminary test for H0:[mu] = [mu]0 is tenable or else towards , is considered a suitable competitor. Certain numerical illustrations are presented showing higher efficiency of such a testimator over in several situations when the sample size is small and [lambda] is either known or unknown.