Matrix-Variate Statistical Distributions and Fractional Calculus

TL;DR

This paper explores the relationship between fractional calculus and matrix-variate statistical distributions, focusing on special functions like Mittag-Leffler and Fox H-functions, with applications in physics such as superstatistics.

Contribution

It extends previous work by establishing new results on matrix-variate densities and their links to fractional calculus, including asymptotic behaviors of generalized Mittag-Leffler densities.

Findings

Connections between fractional calculus and matrix-variate distributions are strengthened.

New properties of generalized Mittag-Leffler densities are derived.

Applications in physics, especially superstatistics, are discussed.

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.