| Multivariate normal distribution | CF | exp ( i μ T t − 1 2 t T Σ t ) {\displaystyle \exp \!{\Big (}i{\boldsymbol {\mu }}^{\mathrm {T} }\mathbf {t} -{\tfrac {1}{2}}\mathbf {t} ^{\mathrm {T} }{\boldsymbol {\Sigma }}\ma… | 1.00 | infobox |
| Multivariate normal distribution | Entropy | k 2 log ( 2 π e ) + 1 2 log det ( Σ ) {\displaystyle {\frac {k}{2}}\log {\mathord {\left(2\pi \mathrm {e} \right)}}+{\frac {1}{2}}\log \det {\mathord {\left({\boldsymbol {\S… | 1.00 | infobox |
| Multivariate normal distribution | Kullback–Leibler divergence | See § Kullback–Leibler divergence | 1.00 | infobox |
| Multivariate normal distribution | Mean | μ | 1.00 | infobox |
| Multivariate normal distribution | MGF | exp ( μ T t + 1 2 t T Σ t ) {\displaystyle \exp \!{\Big (}{\boldsymbol {\mu }}^{\mathrm {T} }\mathbf {t} +{\tfrac {1}{2}}\mathbf {t} ^{\mathrm {T} }{\boldsymbol {\Sigma }}\mathb… | 1.00 | infobox |
| Multivariate normal distribution | Mode | μ | 1.00 | infobox |
| Multivariate normal distribution | Notation | N ( μ , Σ ) {\displaystyle {\mathcal {N}}({\boldsymbol {\mu }},\,{\boldsymbol {\Sigma }})} | 1.00 | infobox |
| Multivariate normal distribution | Parameters | μ ∈ Rk — location Σ ∈ Rk × k — covariance (positive semi-definite matrix) | 1.00 | infobox |
| Multivariate normal distribution | PDF | ( 2 π ) − k / 2 det ( Σ ) − 1 / 2 exp ( − 1 2 ( x − μ ) T Σ − 1 ( x − μ ) ) , {\displaystyle (2\pi )^{-k/2}\det({\boldsymbol {\Sigma }})^{-1/2}\,\exp \left(-{\frac {1}{2}}(\ma… | 1.00 | infobox |
| Multivariate normal distribution | Support | x ∈ μ + span(Σ) ⊆ Rk | 1.00 | infobox |
| Multivariate normal distribution | Variance | Σ, the matrix of individual variances and covariances | 1.00 | infobox |
| Multivariate normal distribution | is a | special case of the Kullback | 0.90 | text |
| Multivariate normal distribution | is a | example of the class of elliptical distributions | 0.90 | text |
