multivariate normal distribution

URI: https://gptkb.org/entity/multivariate_normal_distribution

GPTKB entity

Statements (43)

Predicate	Object
gptkbp:instanceOf	gptkb:organization
gptkbp:alsoKnownAs	gptkb:multivariate_Gaussian_distribution
gptkbp:characteristic	exp(i t^T μ - 1/2 t^T Σ t)
gptkbp:citation	https://en.wikipedia.org/wiki/Multivariate_normal_distribution
gptkbp:conditionalDistribution	gptkb:normal_distribution
gptkbp:covariance	Σ (covariance matrix)
gptkbp:definedIn	n-dimensional real vector space
gptkbp:entropy	(1/2) ln((2πe)^k \|Σ\|)
gptkbp:firstDescribed	19th century
gptkbp:generalizes	gptkb:univariate_normal_distribution
gptkbp:hasInvariant	affine transformations
gptkbp:hasSpecialCase	gptkb:elliptical_distribution
https://www.w3.org/2000/01/rdf-schema#label	multivariate normal distribution
gptkbp:ifCovarianceDiagonal	components are independent
gptkbp:ifCovarianceSingular	distribution is degenerate
gptkbp:kurtosis	3
gptkbp:marginalDistribution	gptkb:normal_distribution
gptkbp:maximumLikelihoodEstimator	sample mean and sample covariance
gptkbp:meaning	μ (mean vector)
gptkbp:moments	all moments exist
gptkbp:namedAfter	gptkb:Carl_Friedrich_Gauss
gptkbp:parameter	covariance matrix mean vector
gptkbp:probabilityDensityFunction	f(x) = (1/((2π)^{k/2} \|Σ\|^{1/2})) exp(-1/2 (x-μ)^T Σ^{-1} (x-μ))
gptkbp:relatedTo	gptkb:Hotelling's_T-squared_distribution gptkb:Mahalanobis_distance gptkb:principal_component_analysis gptkb:Wishart_distribution gptkb:multivariate_t-distribution gptkb:Gaussian_process Bayesian statistics linear discriminant analysis
gptkbp:skewness	0
gptkbp:supports	x ∈ ℝ^k
gptkbp:usedIn	gptkb:machine_learning gptkb:signal_processing engineering finance physics statistics pattern recognition
gptkbp:bfsParent	gptkb:Gaussian_distribution
gptkbp:bfsLayer	5