Multivariate Normal Distribution

The multivariate Normal distribution has the probability density function (PDF):

\[f(x\mid \mu ,\Sigma) = (2\pi)^{-\frac{k}{2}} |\Sigma|^{-\frac{1}{2}} \exp \left(-\frac{1}{2}(x-\mu)^\top \Sigma^{-1}(x-\mu) \right)\]

where \(\mu \in \mathbb{R}^k\) is the mean vector and \(\Sigma \in \mathbb{R}^{k\times k}\) is a positive definite covariance matrix.


e["Distribution"][*index*]["Type"] = "Multivariate/Normal"


These are settings required by this module.

Mean Vector
  • Usage: e[“Mean Vector”] = List of real number

  • Description: Means of the variables.

  • Usage: e[“Sigma”] = List of real number

  • Description: Cholesky Decomposition of the covariance matrix.

  • Usage: e[“Name”] = string

  • Description: Defines the name of the distribution.

Random Seed
  • Usage: e[“Random Seed”] = unsigned integer

  • Description: Defines the random seed of the distribution.

  • Usage: e[“Range”] = gsl_rng

  • Description: Stores the current state of the distribution in hexadecimal notation.

Default Configuration

These following configuration will be assigned by default. Any settings defined by the user will override the given settings specified in these defaults.

"Mean Vector": [],
"Name": "",
"Random Seed": 0,
"Range": "",
"Sigma": []