Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

Details Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

2010-01-13

arxiv.org/abs/1001.2295v1

Proceedings of the Third UN/ESA/NASA Workshop on the International Heliophysical Year 2007 and Basic Space Science, Eds. H.J.

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

12 pages, LaTeX

Scientific paper

Geometric generalized Mittag-Leffler distributions having the Laplace transform $\frac{1}{1+\beta\log(1+t^\alpha)},0<\alpha\le 2,\beta>0$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al (2002, 2004a,b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.

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