Joint Exclusivity

Nawaf Mohammed

Papers from arXiv.org

Abstract: We introduce \emph{joint exclusivity} (JE), a flexible extension of mutual exclusivity for non-negative random vectors that prohibits only the simultaneous positivity of all $n$ components. Unlike mutual exclusivity, JE admits a broad class of marginals while retaining a sharp existence criterion. We prove that a JE random vector with prescribed marginals $F_1,\ldots,F_n$ exists if and only if \[ \sum_{i=1}^n \overline{F}_i(0)\le n-1. \] We also provide a canonical face-based construction with freely specified copulas within each face, and show that the trivariate case can elegantly be reduced to a one-parameter family. Finally, we extend the framework through Wang-type distortions and an $m$-exclusivity hierarchy interpolating between mutual exclusivity and JE.

Date: 2026-04, Revised 2026-08
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