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

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