The moment method (MM) estimator for the shape parameter of generalized Gaussian distribution (GGD) assume asymptotic case when there is available infinite number of observations, but with the smaller sample size the variance of the estimator increases and the moment method equation may not converge to a real solution for some sample sets. The higher order moments can be expanded into series in the moment method equation leading to a drop in the relative mean square error (RMSE) and assuring a solution for a smaller sample size comparing to the moment method without modification.