A universal approach to matching marginals and sums

Robert Griffiths, Kais Hamza

Research output: Contribution to journalArticleResearchpeer-review

Abstract

For a given set of random variables X1, …, Xd we seek as large a family as possible of random variables Y1, …, Yd such that the marginal laws and the laws of the sums match: (Formula Presented) and (Formula Presented).Under the assumption that X1, …, Xd are identically distributed but not necessarily independent, using a symmetry-balancing approach we provide a universal construction with sufficient symmetry to satisfy the more stringent requirement that, for any symmetric function g, (Formula Presented). The same ideas are shown to extend to the non-identically but “similarly” distributed case.

Original languageEnglish
Article number78
Number of pages12
JournalElectronic Communications in Probability
Volume25
DOIs
Publication statusPublished - 2020

Keywords

  • Copula
  • Law of the sum
  • Marginal laws

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