Kshirsagar--Tan independence property of beta matrices and related characterizations
Konstancja Bobecka, Jacek Weso{\l}owski
TL;DR
This paper introduces a novel independence property of beta distributions, characterizes beta laws through this property, and extends the results to certain 2x2 matrices, addressing complex functional equations.
Contribution
It presents a new independence property for beta distributions, characterizes beta laws via this property, and extends the characterization to specific 2x2 matrices, including beta matrices.
Findings
New independence property for univariate beta distributions
Characterization of beta laws through the independence property
Extension to a family of 2x2 matrices including beta matrices
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 random matrices including beta matrices is also obtained. The main technical challenge was a problem involving the solution of a related functional equation.
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