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 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1903-1907. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.