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

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Bobecka, Konstancja
Wesołowski, Jacek
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Abstract
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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.
Comment: Published in at http://dx.doi.org/10.3150/07-BEJ118 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
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Mathematics - Probability, Mathematics - Statistics Theory
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