The information loss in the inverse Gaussian model

In the inverse Gaussian model, the sample mean and sample reciprocal mean a re minimum sufficient, and the distribution of sample reciprocal mean depen ds only on the dispersion parameter. Traditional inference about the disper sion parameter considers only the sample reciprocal mean instead of the who le sufficient statistic. This causes information loss, especially when the sample size is small. The purpose of this paper is to utilize the informati on of the dispersion parameter contained in the sample mean, and to improve the estimation of the dispersion parameter.