Conditional generalized liouville distributions on the simplex

Brian Smith, William Rayens

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Liouville and generalized Liouville distributions on the simplex have been proposed for modeling compositional data and have been shown to be free from the extreme independence structure that characterizes the Dirichlet class. In this article, generalized Liouville distributions are shown to be rich enough to distinguish some lesser modes of independence as well. Unfortunately, it is noted that the applicability of the Liouville family will be limited, owing to the lack of invariance with respect to the chosen fill-up value. As an alternative, a new family of simplex distributions is proposed, one that admits invariance with respect to choice of fill-up value, as well as the ability to differentiate among many forms of independence.

Original languageEnglish
Pages (from-to)185-194
Number of pages10
Issue number2
StatePublished - Jun 2002

Bibliographical note

Funding Information:
During the preparation of this manuscript Professor Rayens was supported by NSF Grant ATM-9108177.

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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