Uniformly Minimum Variance Unbiased Estimation for the Inverse Gaussian Distribution

Abstract

For the inverse Gaussian distribution, we prove a general result concerning the expectation of a certain class of functions of the complete sufficient statistics. Uniformly minimum variance unbiased estimators of the r th cumulant and of several other parametric functions are obtained as special cases. The variance of the estimator for the case r = 2 is also given.