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- 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. The complex Wishart distribution is the density of a complex-valued sample covariance matrix. Let where each is an independent column p-vector of random complex Gaussian zero-mean samples and is an Hermitian (complex conjugate) transpose. If the covariance of G is then where is the complex central Wishart distribution with n degrees of freedom and mean value, or scale matrix, M. where is the complex multivariate Gamma function. Using the trace rotation rule we also get which is quite close to the complex multivariate pdf of G itself. The elements of G conventionally have circular symmetry such that Inverse Complex WishartThe distribution of the inverse complex Wishart distribution of according to Goodman, Shaman is where . If derived via a matrix inversion mapping, the result depends on the complex Jacobian determinant Goodman and others discuss such complex Jacobians. (en)
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- 11293 (xsd:nonNegativeInteger)
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- * is the -variate complex multivariate gamma function
* is the trace function (en)
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- Hermitian positive definite matrix (en)
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| rdfs:comment
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- 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. The complex Wishart distribution is the density of a complex-valued sample covariance matrix. Let where each is an independent column p-vector of random complex Gaussian zero-mean samples and is an Hermitian (complex conjugate) transpose. If the covariance of G is then where is the complex multivariate Gamma function. (en)
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- Complex Wishart distribution (en)
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