Truncation invariant dependence structures

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In this paper, a special class of m-dimensional distribution functions which can be uniquely determined in terms of their 2-dimensional marginals is studied. The members of the class can be characterized as having truncation invariant dependence structure. The representation given in this paper provides a physical meaning to the multivariate Cook-Johnson distribution, and introduces a systematic way of generating higher dimensional distributions by using rich 2-dimensional distributions provided that the 2-dimensional marginals are compatible. A class of 3-dimensional multivariate normal distribution has been generated and bounds in terms of lower dimensional marginals are provided.

Original languageEnglish (US)
Pages (from-to)2553-2568
Number of pages16
JournalCommunications in Statistics - Theory and Methods
Issue number11
StatePublished - 1999


  • 3-dimensional distributions
  • Copulas
  • Multivariate normal distribution
  • The Cook-Johnson distribution
  • Truncated distributions


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