Bivariate distributions with Gaussian-type dependence structure

Shaul K. Bar-Lev, Abram M. Kagan

Research output: Contribution to journalArticlepeer-review


Let Zi=(Xi, Yi), i=1, n be independent random vectors with E|Z i|2. We describe in terms of characteristic functions the distributions of Zi with the following property: all pairs of uncorrelated linear forms L1=a1X1++a nXn and L2=b1Y1++b nYn depending on the first and second components of Z 1, Zn, respectively, are independent. Although the above property formally concerns the dependence structure of the first and second components only, it imposes strict restrictions on the marginal distributions.

Original languageEnglish
Pages (from-to)2669-2676
Number of pages8
JournalCommunications in Statistics - Theory and Methods
Issue number16-17
StatePublished - Jan 2009


  • Dependence
  • Linear forms
  • Vershik's theorem

ASJC Scopus subject areas

  • Statistics and Probability


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