Many sample points from a multivariate normal distribution with and , shown along with the 3-sigma ellipse, the two marginal distributions, and the two 1-d histograms. | |||
Notation | |||
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Parameters | μ ∈ Rk — location Σ ∈ Rk × k — covariance (positive semi-definite matrix) | ||
Support | x ∈ μ + span(Σ) ⊆ Rk | ||
exists only when Σ is positive-definite | |||
Mean | μ | ||
Mode | μ | ||
Variance | Σ | ||
Entropy | |||
MGF | |||
CF | |||
Kullback-Leibler divergence | see below |