Talk:Wishart distribution

message: :
f_{\mathbf W}(w)=
\frac{
  \left|w\right|^{(n-p-1)/2}
  \exp\left[ - {\rm trace}({\mathbf V}^{-1}w/2 )\right] 
}{
2^{np/2}\left|{\mathbf V}\right|^{n/2}\Gamma_p(n/2)
}
shoud be
:
f_{\mathbf W}(w)=
\frac{
  \left|w\right|^{(n-p-1)/2}
  \exp\left[ - \frac{1}{2}{\rm trace}({\mathbf V}^{-1}w )\right] 
}{
2^{np/2}\left|{\mathbf V}\right|^{n/2}\Gamma_p(n/2)
}
?
: Well, the two say exactly the same thing.  Perhaps there is some reason why one way of saying it is preferable in a given context, but certainly if either is correct then so is the other. Michael Hardy 22:37, 18 March 2007 (UTC)
replies: text: Thanks for comments. I confused that  {\rm trace}( A/x )=1/x^p {\rm trace}( A ) . —The preceding unsigned comment was added by 150.29.217.146 (talk) 04:09, 19 March 2007 (UTC)

text: No.  W is the random variable, NOT the argument to the pdf.  Putting the r.v. in that role is a usual clumsy freshman mistake. Michael Hardy (talk) 18:46, 18 September 2008 (UTC)
replies: text:  Using the lower case w notation for the argument is inconsistent and confusing though. How about using something like {\mathbf \Lambda} instead (this would be in keeping with Wishart being the conjugate prior for a multivariate normal with unknown precision matrix) or {\mathbf U} for those who don't like Greek letters. Also note that the argument in Inverse-Wishart distribution is a capital letter. Shae (talk) 08:26, 10 June 2009 (UTC)
thread_title: Untitled

message: I'm assuming that the dagger is indicating the matrix transpose? If it is, then the notation should be changed so that it is consistent with the rest of the article: the superscript "T".  Wtt (talk) 20:20, 27 July 2008 (UTC)
thread_title:  Theorem 

message: I just want to add a theorem that I was looking for a time, and found it. 
Let W=XX^\top an s-by-s matrix, where $X$ is s-by-n (n\geq s) random Gaussian matrix with i.i.d. entries. Then 
: det(W)\sim \prod_{i=1}^{s}\chi^2_{n-i+1}. Zmoboros (talk) 17:06, 27 September 2008 (UTC)
thread_title:  Theorem 

message: I'm wondering if the  \sigma_{jj}  that turns up in Corollary 2 as part of  w_{jj} \sim \sigma_{jj} \chi_m^2  shouldn't have a square on it? Granted  w_{jj}  is the sample variance but is it not  \sigma_{jj}^2  which is the unknown population variance? I think this would be consistent with Corollary 1. Douglas mclean (talk) 08:27, 21 September 2009 (UTC)
thread_title:  Variance or Standard Deviation? 

message: That's another useful contribution!  Coupla points:
- in the Bartlett decomposition, it should be \mathbf{W}, not \mathbf{X}, that is decomposed.
- the decomposition assumes n \ge p.
Primrose61 (talk) 16:23, 28 December 2009 (UTC)
thread_title: Comments

message: Is there a reason for switching from n to m as the d.f. parameter?  (Starting with the first theorem.)  If there isn't a reason for the change, I think it would be better to keep it as n through out.  I can do the change--but I thought I'd ask first since it has been sitting as such for a while it appears.
Dean P Foster (talk) 03:10, 4 April 2010 (UTC)
thread_title: Stupid question

message: Is the missing non-centrality parameter part of an editorial guideline to have separate pages for non-central distributions?  — Preceding unsigned comment added by 92.20.128.145 (talk) 20:40, 20 March 2013 (UTC)
thread_title: Parameters

message: We might want to indicate the measure behind the density. It appears that this is the density against Lebesgue measure on p + (p*(p-1))/2 dimensional real space, the variables corresponding to the lower entries along with the diagonal of the state matrices. However, there are other, possibly more natural, measures to use as an underlying for the space of positive definite symmetric matrices - it could possibly be some curved, invariant measure on the manifold of positive definite symmetric matrices as a subset of p^2 dimensional space (think about how sphere measure is a measure on the 2 dimensional manifold that is a subset of 3 dimensional space that is more natural than, say, Lebesgue measure on the extended complex plane). Perhaps it would be symmetric in the eigenvalues, and symmetric under rotations, etc.Vinzklorthos (talk) 22:33, 6 January 2014 (UTC)
thread_title: Probability density function