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Matrix-variate statistical distributions and fractional calculus

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Abstract

A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results on matrix-variate statistical densities and their connections to fractional calculus will be established. When considering solutions of fractional differential equations, Mittag-Leffler functions and Fox H-function appear naturally. Some results connected with generalized Mittag-Leffler density and their asymptotic behavior will be considered. Reference is made to applications in physics, particularly superstatistics and nonextensive statistical mechanics.

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Authors and Affiliations

  1. Centre for Mathematical Sciences Pala Campus, Arunapuram P.O., Pala, Kerala, 686574, India

    A. M. Mathai

  2. Department of Mathematics and Statistics, McGill University, Montreal, H3A2K6, Canada

    A. M. Mathai

  3. Office for Outer Space Affairs, United Nations, Vienna International Centre, P.O. Box 500, A-1400, Vienna, Austria

    H. J. Haubold

  4. Centre for Mathematical Sciences Pala Campus, Arunapuram P.O., Pala, Kerala, 686574, India

    H. J. Haubold

Authors
  1. A. M. Mathai
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  2. H. J. Haubold
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Correspondence to A. M. Mathai.

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Dedicated to Professor R. Gorenflo on the occasion of his 80th birthday

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Mathai, A.M., Haubold, H.J. Matrix-variate statistical distributions and fractional calculus. fcaa 14, 138–155 (2011). https://doi.org/10.2478/s13540-011-0010-z

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