Multivariate Normal Distribution

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.

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.