On the Uniformly Minimum Variance Unbiased Estimators of the Variance and its Reciprocal of an Inverse Gaussian Distribution

Abstract

Abstract The two-parameter inverse Gaussian distribution is found to have useful applications in a wide variety of fields. The uniformly minimum variance estimator of its mean is known and is the sample mean; however, no such estimator of the variance is reported in the literature. Here the uniformly minimum variance unbiased estimators of the variance and its reciprocal are derived.