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.
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. C33, 81-94,
1984.Schervish, M. J. "Corrections to Multivariate Normal
Probabilities with Error Bounds." Appl. Stat.: J. Roy. Stat. Soc., Ser. C34,
103-104, 1984.Tong, L. The
Multivariate Normal Distribution. New York: Springer-Verlag, 1990.
-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 
).
