A Matsumoto–Yor property for Kummer and Wishart random matrices

Angelo Efoevi Koudou

Statistics & Probability Letters, 2012, vol. 82, issue 11, 1903-1907

Abstract: 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.

Keywords: Wishart distribution; Matsumoto–Yor property; Matrix Kummer distribution; Matrix beta distribution (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spl.2012.06.024

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