Comparison of estimators in stable models

In this paper, several estimators of the index and scale parameter of a symmetric univariate stable distribution are analyzed and compared. It turns out that minimum distance estimators with a suitable choice of the weight function have good theoretical and empirical performance. Also some modifications of the moment method are reliable in large parts of the parameter space. The classical Hill estimator, however, works well only for a small stability index and for an extremely large number of observations. One can construct tail-estimators with a considerably improved behaviour compared to the Hill estimator if the scale is known.