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A -variate multivariate normal distribution (also called a multinormal distribution) is a generalization of the bivariate normal distribution. The -multivariate distribution with mean vector and covariance matrix is denoted . The multivariate normal distribution is implemented as MultinormalDistribution[{mu1, mu2, ...}, {{sigma11, sigma12, ...}, {sigma12, sigma22, ..., }...}, {x1, x2, ...}] in the Wolfram Language package MultivariateStatistics` (where the matrix must be symmetric since ).

In the case of nonzero correlations, there is in general no closed-form solution for the distribution function of a multivariate normal distribution. As a result, such computations must be done numerically.

See also

Bivariate Normal Distribution, Gaussian Joint Variable Theorem, Normal Distribution, Trivariate Normal Distribution

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References

Rose, C. and Smith, M. D. "The Multivariate Normal Distribution." Mathematica J. 6, 32-37, 1996.Rose, C. and Smith, M. D. "Random[Title]: Manipulating Probability Density Functions." Ch. 16 in Computational Economics and Finance: Modeling and Analysis with Mathematica (Ed. H. Varian). New York: Springer-Verlag, 1996.Rose, C. and Smith, M. D. "The Multivariate Normal Distribution." §6.4 in Mathematical Statistics with Mathematica. New York: Springer-Verlag, pp. 216-235, 2002.Schervish, M. J. "Multivariate Normal Probabilities with Error Bounds." Appl. Stat.: J. Roy. Stat. Soc., Ser. C 33, 81-94, 1984.Schervish, M. J. "Corrections to Multivariate Normal Probabilities with Error Bounds." Appl. Stat.: J. Roy. Stat. Soc., Ser. C 34, 103-104, 1984.Tong, L. The Multivariate Normal Distribution. New York: Springer-Verlag, 1990.

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Multivariate Normal Distribution

Cite this as:

Weisstein, Eric W. "Multivariate Normal Distribution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MultivariateNormalDistribution.html

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