On notions of Q-independence and Q-identical distributiveness

TL;DR

This paper characterizes the polynomials involved in the definitions of Q-independence and Q-identical distribution, clarifying the mathematical structure behind these concepts introduced by Kagan and Székely.

Contribution

It provides a complete description of the polynomials used in the notions of Q-independence and Q-identical distribution, advancing the theoretical understanding of these concepts.

Findings

Characterization of polynomials in Q-independence

Characterization of polynomials in Q-identical distribution

Clarification of the mathematical structure of Q-concepts

Abstract

In a recent article A.M. Kagan and G.J.Sz\'ekely introduced a notion of Q-independent and Q-identical distributed random variables. We give a complete description of polynomials which appear in these definitions.