MATRIX-VARIATE STATISTICAL DISTRIBUTIONS AND FRACTIONAL CALCULUS

作者：Mathai A M^*; Haubold H J

来源：Journal of Fractional Calculus and Applied Analysis, 2011, 14(1): 138-155.

DOI：10.2478/s13540-011-0010-z

• fractional calculus
• matrix-variate statistical distributions
• pathway model
• Fox H-function
• Mittag-Leffler function
• Levy density
• Kratzel integral
• extended beta models

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.

• 出版日期2011-3