pdfWishartInv#

Purpose#

Computes the probability density function of the inverse Wishart distribution.

Format#

p = pdfWishartInv(IW, S, df)#

Parameters:

IW (p x p positive definite matrix) – \(T\), the values used to compute the inverse Wishart distribution.
S (p x p matrix) – \(\Psi\), the positive definite scale matrix parameter
df (Scalar) – \(\nu\), degrees of freedom.

Returns:

p (Scalar) – probability density function.

Examples#

new ;
cls ;
rndseed 2223;

x = {9.2517907  7.4283670,
     7.4283670 10.503325 };

S = {1 .5, .5 1};

df = 3;

// pdf of inverse Wishart distribution
y = pdfWishartInv(x, S, df);

print y;

After above code,

6.0267322e-007

Remarks#

pdfWishartInv calculates the probability density function for the inverse Wishart distribution, which is defined as

\[f(T;\Psi,\nu) = \frac{|\Psi^{\frac{\nu}{2}}|}{2^{\nu p/2}\Gamma_p(\frac{\nu}{2})}|T|^{-(\nu+p+1)/2} e^{-\frac{1}{2}tr(\Psi T^{-1})}\]