Minimum discrimination information estimator of the inverse Gaussian mean with known coefficient of variation

We deal with the estimation of the mean of an inverse Gaussian distribution with known coefficient of variation. Applying the minimum discrimination information (MDI) method, the MDI estimator for the mean is derived and its asymptotic variance is presented. The behavior of the derived estimator is examined on the basis of large sample. Monte Carlo simulations are conducted to investigate the small sample performance of the MDI estimator compared to other estimators including the maximum likelihood estimator for the different values of sample size and coefficient of variation. MSE efficiency of the MDI estimator is shown to be higher than its competitor estimators.