Kumaraswamy and beta distribution are related by the logistic map

TL;DR

This paper reveals a novel connection between Kumaraswamy and beta distributions through the logistic map, a fundamental example of nonlinear dynamical systems, expanding understanding of their mathematical relationship.

Contribution

It introduces a new relationship between Kumaraswamy and beta distributions using the logistic map, beyond the previously known algebraic transformation.

Findings

Established a relationship via the logistic map

Extended the understanding of distribution connections

Potential implications for nonlinear dynamical systems

Abstract

The Kumaraswamy distribution has been proposed as an alternative to the beta distribution with more benign algebraic properties. They have the same two parameters, the same support and qualitatively similar shape for any parameter values. There is a generic relationship between the distributions established by a simple transformation between arbitrary Kumaraswamy-distributed random variables and certain beta-distributed random variables. Here, a different relationship is established by means of the logistic map, the paradigmatic example of a discrete non-linear dynamical system.