Joint mixability of elliptical distributions and related families

TL;DR

This paper explores the joint mixability of elliptical and related distributions, providing new proofs, generalizations, and solutions to open problems, including the study of skewed and slash-elliptical distributions and their multivariate extensions.

Contribution

It offers new proofs of existing results, generalizes joint mixability to distributions with finite second moments, and constructs solutions to open problems involving bimodal and skewed distributions.

Findings

Proved three different proofs for a key joint mixability result.

Generalized joint mixability to any distributions with finite second moments.

Constructed a bimodal-symmetric distribution solving an open problem.

Abstract

In this paper, three different proofs to a result of Wang, Peng and Yang (2013) which related to the joint mixability of elliptical distributions with the same characteristic generator are present. Moreover, we generalize this result to any distributions with finite second moments. An open problem proposed by Wang (2015) is solved by constructing a bimodal-symmetric distribution. The joint mixability of slash-elliptical distributions and skew-elliptical distributions is studied and the extension to multivariate distributions is also investigated.