On a new approach to estimate the shape parameter of the inverse Gaussian distribution

In this paper, we propose a new simple method for estimating the shape parameter of the inverse Gaussian distribution. This new method makes use of the reciprocal property of the distribution. Also, bias-reduced versions of this proposed estimator are introduced. Furthermore, a new test for the coefficient of variation in an inverse Gaussian distribution is derived. The performance of the estimators are evaluated via Monte Carlo simulations. In general, compared with the maximum likelihood estimator, the proposed method has smaller bias. Two real data sets are used to illustrate the proposed methodology.