Elliptical invariance of distributions of the power type: the stability and extensivity issues

TL;DR

This paper investigates the stability and extensivity properties of power-type probability distributions, focusing on their behavior as maximizers of generalized information measures under addition and composition processes.

Contribution

It provides new insights into the stability and invariance properties of power-type distributions, addressing recent questions in the literature.

Findings

Power-type distributions are stable under addition and composition.

Maximizers of generalized information measures exhibit elliptical invariance.

Results clarify stability and extensivity issues of these distributions.

Abstract

In this paper we delve into some important properties of probability distributions of the power type in order to provide some answers to questions recently raised in the literature. More precisely, we focus on the properties of maximizers of generalized information measures and give results about their stability under addition-composition processes.