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wishart.rst

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Wishart Distribution

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The density function of the Wishart distribution:

f(\mathbf{X}; \boldsymbol{\Psi}, \nu) = \dfrac{1}{2^{\frac{\nu p}{2}} |\boldsymbol{\Psi}|^{\frac{\nu}{2}} \Gamma_p\left( \frac{\nu}{2} \right)} | \mathbf{X} |^{\frac{\nu - p - 1}{2}} \exp \left( - \frac{1}{2} \text{tr} (\boldsymbol{\Psi}^{-1} \mathbf{X}) \right)

where \Gamma_p is the Multivariate Gamma function, | \cdot | denotes the matrix determinant, and \text{tr}(\cdot) denotes the matrix trace.

.. doxygenfunction:: dwish(const mT&, const mT&, const pT, const bool)
   :project: statslib


.. doxygenfunction:: rwish(const mT&, const pT, rand_engine_t&, const bool)
   :project: statslib