Fractional moment estimation of linnik and mittag-leffler parameters

Authors:
T. J. Kozubowski
Affiliations:
Department of Mathematics University of Nevada Reno, NV 89557, USA
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2001

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Abstract

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.