Sequential Estimation of an Inverse Gaussian Mean with Known Coefficient of Variation

This paper deals with developing sequential procedures for estimating the mean of an inverse Gaussian (IG) distribution when the population coefficient of variation (CV) is known. We consider the minimum risk and bounded risk point estimation problems respectively. Moreover, we make use of a weighted squared-error loss function and aim to control the associated risk functions. Instead of the usual estimator, i.e., the sample mean, Searls J. Amer. Stat. Assoc. 50, 1225–1226 (1964) estimator is utilized for the purpose of estimation. Second-order approximations are also obtained under both estimation set-ups. We establish that Searls’ estimator dominates the usual estimator (sample mean) under proposed sequential sampling procedures. An extensive simulation analysis is carried out to validate the theoretical findings and real data illustrations are also provided to show the practical utility of our proposed sequential stopping strategies.