A new independence property of univariate beta distributions, related to the results of Kshirsagar and Tan for beta matrices, is presented. Conversely, a characterization of univariate beta laws through this independence property is proved. A related characterization of a family of 2×2 random matrices including beta matrices is also obtained. The main technical challenge was a problem involving the solution of a related functional equation.
Publié le : 2008-08-15
Classification:
beta matrix,
Dirichlet distribution,
functional equations,
independence,
perpetuities,
univariate beta distribution
@article{1219669628,
author = {Bobecka, Konstancja and Weso\l owski, Jacek},
title = {Kshirsagar--Tan independence property of beta matrices and related characterizations},
journal = {Bernoulli},
volume = {14},
number = {1},
year = {2008},
pages = { 749-763},
language = {en},
url = {http://dml.mathdoc.fr/item/1219669628}
}
Bobecka, Konstancja; Wesołowski, Jacek. Kshirsagar–Tan independence property of beta matrices and related characterizations. Bernoulli, Tome 14 (2008) no. 1, pp. 749-763. http://gdmltest.u-ga.fr/item/1219669628/