Estimation of parameters for generalized Gaussian distribution

Shape parameter estimation procedures for generalized Gaussian distribution are considered. It is shown that the existing estimators can be divided into four groups: maximum likelihood algorithm; moment-based methods; entropy matching estimators and global convergence algorithm. Besides, properties of two recently introduced estimators of shape parameter are discussed. They are based on the combination of two procedures that use the evaluation of the fourth central moment and robust measure of kurtosis. Statistical properties of all considered estimators are investigated by means of defining their bias and variance values for samples of sizes 1000 and 4000 elements and shape parameter values ranging from 0.3 to 2.