Fractional moment estimation of Linnik and Mittag-Leffler parameters

It is shown that Linnik and Mittag-Leffler distributions are geometric stab le (GS). An estimation method for the parameters of Linnik and Mittag-Leffi er distributions, based on fractional moments, is proposed. Algorithms for simulation of Linnik and Mittag-Leffler distributions, based on their repre sentations as mixtures of Laplace and exponential distributions, are presen ted. The estimation procedure is validated on simulated data, and its poten tial applications are illustrated with S&P index data, that is shown to be consistent with a two-parameter Linnik model. (C) 2001 Elsevier Science Ltd . All rights reserved.