Kshirsagar--Tan independence property of beta matrices and related characterizations

Details Kshirsagar--Tan independence property of beta matrices and related characterizations Kshirsagar--Tan independence property of beta matrices and related characterizations

2008-10-24

arxiv.org/abs/0810.4427v1

Bernoulli 2008, Vol. 14, No. 3, 749-763

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/07-BEJ118 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/07-BEJ118

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 $2\times2$ 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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