Editing Wishart distribution (section)

==Definition==
Suppose {{mvar|G}} is a {{math|''p'' × ''n''}} matrix, each column of which is [[statistical independence|independently]] drawn from a [[multivariate normal distribution|{{mvar|p}}-variate normal distribution]] with zero mean:

:<math>G = (g_i^1,\dots,g_i^n) \sim \mathcal{N}_p(0,V).</math>

Then the Wishart distribution is the [[probability distribution]] of the {{math|''p'' × ''p''}} random matrix <ref>{{cite book |first1=A. K. |last1=Gupta |first2=D. K. |last2=Nagar |date=2000 |title=Matrix Variate Distributions |publisher=Chapman & Hall /CRC |isbn=1584880465}}</ref>

:<math>S= G G^T = \sum_{i=1}^n g_{i}g_{i}^T</math>

known as the [[scatter matrix]]. One indicates that {{mvar|S}} has that probability distribution by writing

:<math>S\sim W_p(V,n).</math>

The positive integer {{mvar|n}} is the number of ''[[degrees of freedom (statistics)|degrees of freedom]]''.  Sometimes this is written {{math|''W''(''V'', ''p'', ''n'')}}. For {{math|''n'' ≥ ''p''}} the matrix {{mvar|S}} is invertible with probability {{math|1}} if {{mvar|V}} is invertible.

If {{math|''p'' {{=}} ''V'' {{=}} 1}} then this distribution is a [[chi-squared distribution]] with {{mvar|n}} degrees of freedom.