The Covariance Structure of the Multivariate Liouville Distributions
by
Rameshwar D. Gupta
Department of Comp. Sc. & Applied Statistics, University of New Brunswick
Coauthors: Donald St. P. Richards (Department of Statistics, Penn State University)

We study the covariance structure of the multivariate Liouville distributions and their power-scale transformations. For any Liouville distributions, we show that the off-diagonal entries of the corresponding correlation matrix all have the same sign; and we show that this result holds also for power-scale transformations of the Dirichlet distributions. In the case of matrix Dirichlet distributions, we derive formulas for the all moments of degree one and two, leading to the discovery of some remarkable relationships among the underlying covariances; in particular, we deduce that the resulting covariance matrices are of block-diagonal form. In the case of the matrix Liouville distributions we also drive formulas for all moments of degree one and two, thereby deducing completely their covariance structure.

Date received: October 24, 2002