A Matsumoto–Yor property for Kummer and Wishart random matrices
For a positive integer r, let I denote the r×r unit matrix. Let X and Y be two independent r×r real symmetric and positive definite random matrices. Assume that X follows a Kummer distribution while Y follows a non-degenerate Wishart distribution, with suitable parameters. This note points out the following observation: the random matrices U:=[I+(X+Y)−1]1/2[I+X−1]−1[I+(X+Y)−1]1/2 and V:=X+Y are independent and U follows a matrix beta distribution while V follows a Kummer distribution. This generalizes to the matrix case an independence property established in Koudou and Vallois (2010) for r=1.
Volume (Year): 82 (2012)
Issue (Month): 11 ()
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- Massam, Hélène & Wesolowski, Jacek, 2006. "The Matsumoto-Yor property and the structure of the Wishart distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 103-123, January.
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