Maximum entropy characterizations of the multivariate Liouville distributions |
| |
Authors: | Bhaskar Bhattacharya |
| |
Institution: | Department of Mathematics, Southern Illinois University, Carbondale, IL 62901-4408, USA |
| |
Abstract: | 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 , 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. |
| |
Keywords: | 62E10 62H10 62B10 |
本文献已被 ScienceDirect 等数据库收录! |
|