The mixability of elliptical distributions and log-elliptical distributions

TL;DR

This paper explores the concept of $\,\phi$-joint mixability in elliptical and log-elliptical distributions, providing conditions for mixability, conjectures on uniqueness, and characterizations of density forms.

Contribution

It extends the theory of $\,\phi$-joint mixability to elliptical and log-elliptical distributions, offering new sufficient conditions and conjectures.

Findings

Established sufficient conditions for $\,\phi$-joint mixability.

Proposed a conjecture on the uniqueness of the center.

Characterized the density forms for certain elliptical distributions.

Abstract

The concept of $\phi$-complete mixability and $\phi$-joint mixability was first introduced in Bignozzi and Puccetti (2015), which is an extension of complete and joint mixability. Following Bignozzi and Puccetti (2015), we consider two more general cases of $\phi$ and investigate the $\phi$-joint mixability for elliptical distributions and logarithmic elliptical distributions. Some sufficient conditions for the $\phi$-joint mixability of some distributions are investigated. In addition, a conjecture on the uniqueness of the center of $\phi$-joint mixability and the forms of the densities for some elliptical distributions are given.