MultinormalDistribution

The multivariate normal with mean vector $\mu$ and covariance matrix $\Sigma$ ; the one-argument form defaults $\mu$ to the zero vector.

MultinormalDistribution(mu, Sigma)mean mu, covariance Sigma.

MultinormalDistribution(Sigma)mean the zero vector, covariance Sigma.

Typed signatures

Type	Package	Applies
`((list<list<real>>) -> distribution) & ((list<real>, list<list<real>>) -> distribution)`	`statistics`	always

Domain: Statistics

Details

$PDF(x) = (2\pi)^{-k/2} |\Sigma|^{-1/2} \exp\left(-\tfrac12 (x-\mu)^T \Sigma^{-1} (x-\mu)\right)$ — exact whenever $\Sigma$ is rational, via compute-engine's own native Determinant/Inverse/Dot, which stay exact over rationals.
$Mean = \mu$ . $Variance$ is the DIAGONAL of $\Sigma$ (a length- $k$ list) — Wolfram's own convention; the full matrix is Covariance (see below).
Covariance (compute-engine native over two collections) is widened to also accept a single MultinormalDistribution, answering $\Sigma$ itself.
RandomVariate draws $x = \mu + Lz$ , $z$ iid standard normal, $L$ the (numeric) Cholesky factor of $\Sigma$ — the standard construction, seeded through the same SeedRandom stream every other distribution in this package uses.