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.
|Number of pages||10|
|State||Published - Jun 2002|
Bibliographical noteFunding 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