Abstract
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.
Citation
Konstancja Bobecka. Jacek Wesołowski. "Kshirsagar–Tan independence property of beta matrices and related characterizations." Bernoulli 14 (3) 749 - 763, August 2008. https://doi.org/10.3150/07-BEJ118
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