The Stein Characterization of $M$-Wright Distributions

TL;DR

This paper employs the Stein method to characterize the $M$-Wright distribution and its symmetrization, linking it to the Airy equation, providing a new analytical perspective on these distributions.

Contribution

It introduces a Stein characterization for the $M$-Wright distribution using the Airy equation, a novel approach in distribution analysis.

Findings

Stein operator linked to the Airy equation for $M$-Wright distribution

Derivation of a Stein equation as an inhomogeneous Airy equation

Provides a new analytical tool for studying $M$-Wright distributions

Abstract

In this paper use the Stein method to characterize the $M$-Wright distribution $M_{\frac{1}{3}}$ and its symmetrization. The Stein operator is associated with the general Airy equation and the corresponding Stein equation is nothing but a general inhomogeneous Airy equation.