Joint Exclusivity

TL;DR

This paper introduces joint exclusivity, a new form of negative dependence extending mutual exclusivity, with a tractable structure, existence conditions, and connections to joint mixability.

Contribution

It defines joint exclusivity, provides a construction method, extends it to G-JE, and reveals its structural link to joint mixability.

Findings

Established a necessary and sufficient condition for JE existence.

Proposed a canonical probability distribution construction.

Linked JE support structures to joint mixability.

Abstract

We introduce joint exclusivity (JE), a form of extremal negative dependence that extends the classical notion of mutual exclusivity. The JE structure is analytically tractable and is defined by the exclusion of the interior of the non-negative orthant. We establish a sharp necessary and sufficient condition for the existence of a JE random vector with prescribed marginals, namely $\sum_{i\in N} \overline{F}_i(0) \leq n - 1$. We propose a canonical construction that distributes probability mass on lower-dimensional faces of the support, while allowing flexible copula specifications within each face. The framework is further extended to a generalized class (G-JE) via marginal distortion functions. Finally, we identify a correspondence between the support structures of JE and joint mixability, revealing a structural link between the two concepts.