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

Konstancja Bobecka; Jacek Wesołowski

doi:10.3150/07-BEJ118

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

Probability 2008-10-27 v1 Statistics Theory Statistics Theory

Authors: Konstancja Bobecka , Jacek Wesołowski

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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 $2\times2$ random matrices including beta matrices is also obtained. The main technical challenge was a problem involving the solution of a related functional equation.

Keywords

beta distribution independence property beta matrix characterization functional equation random matrix

Cite

@article{arxiv.0810.4427,
  title  = {Kshirsagar--Tan independence property of beta matrices and related characterizations},
  author = {Konstancja Bobecka and Jacek Wesołowski},
  journal= {arXiv preprint arXiv:0810.4427},
  year   = {2008}
}

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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)

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

Abstract

Keywords

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