Multivariate Liouville distributions
Journal of Multivariate Analysis
Entropy inequalities for some multivariate distributions
Journal of Multivariate Analysis
On maximum entropy characterization of Pearson's type II and VII multivariate distributions
Journal of Multivariate Analysis
Entropy expressions for multivariate continuous distributions
IEEE Transactions on Information Theory
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A random vector X = (X1, X2,...,Xn) with positive components has a Liouville distribution with parameter θ = (θ1, θ2,...,θn) if its joint probability density function is proportional to h(Σi=1n xi) Φi=1n xiθi-1, θi 0 [R.D. Gupta, D.S.P. Richards, Multivariate Liouville distributions, J. Multivariate Anal. 23 (1987) 233-256]. Examples include correlated gamma variables, Dirichlet and inverted Dirichlet distributions. We derive appropriate constraints which establish the maximum entropy characterization of the Liouville distributions among all multivariate distributions. Matrix analogs of the Liouville distributions are considered. Some interesting results related to I-projection from a Liouville distribution are presented.