On estimating common mean of several inverse Gaussian distributions

Estimation of the common mean of inverse Gaussian distributions with different scale-like parameters is considered. We study finite sample properties, second-order admissibility and Pitman closeness properties of the Graybill-Deal estimator of the common mean. The best asymptotically normal estimator of the common mean is derived when the coefficients of variations are known. When the scale-like parameters are unknown but ordered, an improved estimator of the common mean is proposed. We also derive estimators of the common mean using the modified profile likelihood method. A simulation study has been performed to compare among the estimators.