Joint Exclusivity

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.