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B0459
**Title: **A Matsumoto-Yor characterization for Kummer and Wishart random matrices
**Authors: **Bartosz Kolodziejek - Warsaw University of Technology (Poland) **[presenting]**

**Abstract: **For independent $X$ and $Y$ with Kummer and gamma distributions, respectively, random variables $U=(1+1/(X+Y))/(1+1/X)$ and $V=X+Y$ have been proved to be also independent. This property was later generalized to random matrices $X$ and $Y$ with matrix Kummer and Wishart laws. The aim is to give a converse result in a matrix-variate framework. Such a characterization of matrix Kummer and Wishart laws is proved under the assumption that the densities of $X$ and $Y$ exist and are continuous and strictly positive one some sets. The proof uses the solution to related functional equation with matrix arguments.