Minimum risk scale equivariant estimator: estimating the mean of an inverse gaussian distribution with known coefficient of variation

Abstract

An estimation problem of the mean μ of an inverse Gaussian distribution I(μa^-2μ) with known coefficient of variation a is discussed. The minimum risk scale equivariant estimator is derived by using a loss function which is invariant under scale changes and is well balanced between errors for small and large values of a positive parameter. It is shown that is represented as a continued fraction and dominates the maximum likelihood estimator in risk. The minimum risk scale equivariant estimator under the loss function above is given as a Pitman estimator of scale parameter.

Keywords:

• Inverse gaussian distribution
• scale equivariant estimator
• loss function
• pitman estimator
• ancillary statistic
• known coefficient of variation