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Axioms 2015, 4(3), 365-384; doi:10.3390/axioms4030365

An Overview of Generalized Gamma Mittag–Leffler Model and Its Applications

St. Gregorios College, Kottarakara, Kerala 691531, India
Academic Editor: Hans J. Haubold
Received: 6 May 2015 / Revised: 23 July 2015 / Accepted: 27 July 2015 / Published: 26 August 2015
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Abstract

Recently, probability models with thicker or thinner tails have gained more importance among statisticians and physicists because of their vast applications in random walks, Lévi flights, financial modeling, etc. In this connection, we introduce here a new family of generalized probability distributions associated with the Mittag–Leffler function. This family gives an extension to the generalized gamma family, opens up a vast area of potential applications and establishes connections to the topics of fractional calculus, nonextensive statistical mechanics, Tsallis statistics, superstatistics, the Mittag–Leffler stochastic process, the Lévi process and time series. Apart from examining the properties, the matrix-variate analogue and the connection to fractional calculus are also explained. By using the pathway model of Mathai, the model is further generalized. Connections to Mittag–Leffler distributions and corresponding autoregressive processes are also discussed. View Full-Text
Keywords: generalized Mittag–Leffler density and process; gamma density; Lévi density; pathway model; Tsallis statistics; superstatistics generalized Mittag–Leffler density and process; gamma density; Lévi density; pathway model; Tsallis statistics; superstatistics
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Nair, S.S. An Overview of Generalized Gamma Mittag–Leffler Model and Its Applications. Axioms 2015, 4, 365-384.

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