Complex Wishart distribution

Complex Wishart

Notation	A ~ CWp($\Gamma$, n)
Parameters	n > p − 1 degrees of freedom (real) $\Gamma$ > 0 (p × p Hermitian pos. def)
Support	A (p × p) Hermitian positive definite matrix
PDF	${\frac {\det \left(\mathbf {A} \right)^{(n-p)}e^{-\operatorname {tr} (\mathbf {\Gamma } ^{-1}\mathbf {A} )}}{\det \left(\mathbf {\Gamma } \right)^{n}\cdot {\widetilde {\Gamma }}_{p}(n)}}$ ${\widetilde {\mathbf {\Gamma } }}_{p}$ is the $p$-variate complex multivariate gamma function tr is the trace function
Mean	$\operatorname {E} [A]=n\Gamma$
Mode	$(n-p)\mathbf {\Gamma }$ for n ≥ p + 1
CF	$\det \left(I_{p}-i\mathbf {\Gamma } \mathbf {\Theta } \right)^{-n}$

In statistics, the complex Wishart distribution is a complex version of the Wishart distribution. It is the distribution of $n$ times the sample Hermitian covariance matrix of $n$ zero-mean independent Gaussian random variables. It has support for $p\times p$ Hermitian positive definite matrices.