Mittag-Leffler Probability Density for Nonextensive Statistics and Superstatistics

TL;DR

This paper explores the properties of Mittag-Leffler probability densities, their structural representations, and their connections to nonextensive statistics and superstatistics, highlighting their non-Gaussian limit behaviors and mathematical pathways.

Contribution

It introduces a structural representation of Mittag-Leffler variables and links them to nonextensive statistics and superstatistics through mathematical pathways.

Findings

Mittag-Leffler density has unique properties and representations.

Limit theorems lead to positive Levy distributions instead of Gaussian.

Constructs pathways connecting Mittag-Leffler functions to superstatistics.

Abstract

It is shown that a Mittag-Leffler density has interesting properties. The Mittag-Leffler random variable has a structural representation in terms of a positive Levy variable and the power of a gamma variable where these two variables are independently distributed. It is shown that several central limit-type properties hold but the limiting forms are positive Levy variable rather than a Gaussian variable. A path is constructed from a Mittag-Leffler function to the Mathai pathway model which also provides paths to nonextensive statistics and superstatistics.