Paper: arXiv 2604.17490

Authors: Nawaf Mohammed

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a highly novel mathematical concept (Joint Exclusivity) and establishes rigorous theoretical bounds and structural links with joint mixability. However, it is purely theoretical with no empirical backtests, market datasets, or quantitative financial applications presented in the excerpt.

Research Flowchart

  flowchart TD
    A["Research Goal: Define & analyze Joint Exclusivity (JE) for extremal negative dependence"] --> B["Input: Prescribed marginal distributions F_i(x) and non-negative orthant constraint"]
    B --> C["Existence Condition: Verify if ∑ F̄_i(0) ≤ n - 1"]
    C --> D["Canonical Construction: Distribute probability mass on lower-dimensional faces with flexible copulas"]
    D --> E["Extensions: Apply marginal distortion functions for Generalized JE (G-JE)"]
    E --> F["Key Outcomes: Tractable JE framework & proven structural link between JE and Joint Mixability"]

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2 of 723 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.