Complex Wishart distribution

Complex Wishart
Notation A ~ CWp( , n)
Parameters n > p − 1 degrees of freedom (real)
> 0 (p × p Hermitian pos. def)
Support A (p × p) Hermitian positive definite matrix
PDF

  • is the -variate complex multivariate gamma function
  • tr is the trace function
Mean
Mode for np + 1
CF

In statistics, the complex Wishart distribution is a complex version of the Wishart distribution. It is the distribution of times the sample Hermitian covariance matrix of zero-mean independent Gaussian random variables. It has support for Hermitian positive definite matrices.[1]

References

  1. N. R. Goodman (1963). "The distribution of the determinant of a complex Wishart distributed matrix". The Annals of Mathematical Statistics. 34 (1). pp. 178–180.
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