multivariate-normal.rst

Multivariate-Normal Distribution

Table of contents

• Density Function
• Random Sampling

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Density Function

The density function of the Multivariate-Normal distribution:

f(\mathbf{x}; \boldsymbol{\mu}, \boldsymbol{\Sigma}) = \dfrac{1}{\sqrt{(2\pi)^k |\boldsymbol{\Sigma}|}} \exp \left( - \frac{1}{2} (\mathbf{x} - \boldsymbol{\mu})^\top \boldsymbol{\Sigma}^{-1} (\mathbf{x} - \boldsymbol{\mu}) \right)

where k is the dimension of the real-valued vector \mathbf{x} and | \cdot | denotes the matrix determinant.

.. doxygenfunction:: dmvnorm(const vT&, const vT&, const mT&, const bool)
   :project: statslib

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Random Sampling

.. doxygenfunction:: rmvnorm(const vT&, const mT&, rand_engine_t&, const bool)
   :project: statslib