Generalization of the one-dimensional normal distribution to higher dimensions
Multivariate normal
Probability density function
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.
In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem. The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables, each of which clusters around a mean value.
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theory and statistics, the multivariatenormaldistribution, multivariate Gaussian distribution, or joint normaldistribution is a generalization of the...
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matrix normaldistribution or matrix Gaussian distribution is a probability distribution that is a generalization of the multivariatenormaldistribution to...
modern, overlapping categorization of MVA includes: Normal and general multivariate models and distribution theory The study and measurement of relationships...
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Complex normal ratio distribution Directional statistics § Distribution of the mean (polar form) NormaldistributionMultivariatenormaldistribution (a complex...
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dependent variables whose linear combination follows a multivariatenormaldistribution, multivariate variance-covariance matrix homogeneity, and linear relationship...
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generalized normaldistribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the...
the binomial distribution. The multivariatenormaldistribution, a generalization of the normaldistribution. The multivariate t-distribution, a generalization...
and statistics, the skew normaldistribution is a continuous probability distribution that generalises the normaldistribution to allow for non-zero skewness...
then it naturally becomes singular. The FIM for a N-variate multivariatenormaldistribution, X ∼ N ( μ ( θ ) , Σ ( θ ) ) {\displaystyle \,X\sim N\left(\mu...
the actual covariance matrix on the basis of a sample from the multivariatedistribution. Simple cases, where observations are complete, can be dealt with...
continuous multivariate probability distributions parameterized by a vector α {\displaystyle {\boldsymbol {\alpha }}} of positive reals. It is a multivariate generalization...
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![{\displaystyle {\boldsymbol {\mu }}=\left[{\begin{smallmatrix}0\\0\end{smallmatrix}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/288f20c89fee827ad086cec03369439ba3615d7f)
![{\displaystyle {\boldsymbol {\Sigma }}=\left[{\begin{smallmatrix}1&3/5\\3/5&2\end{smallmatrix}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee3a76f734b37fcce91f30617152fe104b2782bc)
