Fractional moment estimation of linnik and mittag-leffler parameters

It is shown that Linnik and Mittag-Leffler distributions are geometric stable (GS). An estimation method for the parameters of Linnik and Mittag-Leffler distributions, based on fractional moments, is proposed. Algorithms for simulation of Linnik and Mittag-Leffler distributions, based on their representations as mixtures of Laplace and exponential distributions, are presented. The estimation procedure is validated on simulated data, and its potential applications are illustrated with S&P index data, that is shown to be consistent with a two-parameter Linnik model.