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A Matsumoto–Yor property for Kummer and Wishart random matrices

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  • Koudou, Angelo Efoevi
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 11 ()
    Pages: 1903-1907

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1903-1907

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    Related research

    Keywords: Wishart distribution; Matsumoto–Yor property; Matrix Kummer distribution; Matrix beta distribution;

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    1. 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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