This paragraph replaces a previous subsection in the article "Multivariate t-distribution".

Conditional Distribution

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This was demonstrated by Muirhead [1] though previously derived using the simpler ratio representation above, by Cornish.[2] Let vector   follow the multivariate t distribution and partition into two subvectors of   elements:

 

where  , the known mean vector is   and the scale matrix is  .

Then

 

explicitly

 

where

  is the conditional mean
  is the Schur complement of  
  is the squared Mahalanobis distance of   from   with scale matrix  
  1. ^ Muirhead, Robb (1982). Aspects of Multivariate Statistical Theory. USA: Wiley. pp. 32–36 Theorem 1.5.4. ISBN 978-0-47 1-76985-9.
  2. ^ Cornish, E A (1954). "The Multivariate t-Distribution Associated with a Set of Normal Sample Deviates". Australian Journal of Physics. 7: 531–542. doi:10.1071/PH550193.