Command Reference : Function Reference : Function Reference: R
  
 
@rwish
Wishart random draw.
Syntax: @rwish(S, n)
@rwishc(S, n)
@rwishi(S, n)
@rwishic(S, n)
X: (optional) sym,
S: sym, matrix,
n: number,
Return: sym
Draw a random symmetric Wishart matrix using the density function.
The Wishart density is given by
where and are symmetric matrices, and .
There are four different forms of the function, corresponding to different ways of specifying . The forms are distinguished by different suffixes that are applied to the base “@rwish” command and how they change the interpretation of the S matrix argument:
 
@rwish
“”
Supply .
@rwishc
“c”
Supply the Cholesky decomposition of .
This form is more efficient when performing multiple draws from the same distribution (compute the Cholesky once, but sample many times).
@rwishi
“i”
Supply .
This form is more efficient than explicitly inverting to supply .
@rwishic
“ic”
Supply the Cholesky decomposition of .
This form combines the efficiencies of the Cholesky and inverse forms.
is generally thought of as the accumulated scatter matrix of n random draws from , i.e., ,
,
though the mathematical definition has been extended to cover real-valued n.
Note that if is a Wishart random variable, then follows an inverse Wishart distribution:
Examples
= @rwish(@identity(3), 5)
returns a random draw from the distribution.
Cross-references
See also @dwish, @diwish, and @riwish.