Multivariate Statistics Package Symbol

MultinormalDistribution

MultinormalDistribution[

,

]
represents a multivariate normal (Gaussian) distribution with mean vector

and covariance matrix

.

To use MultinormalDistribution, you first need to load the Multivariate Statistics Package using Needs["MultivariateStatistics`"].

The probability density for vector x in a multivariate normal distribution is proportional to ^{-(x-).^-1.(x-)/2}.

The mean can be any vector of real numbers, and can be any symmetric positive definite p×p matrix with p=Length[].

MultinormalDistribution can be used with such functions as Mean, CDF, and RandomReal.

The mean of a bivariate normal distribution with correlation

:

The variances of each dimension:

Probability density function:

Needs["MultivariateStatistics`"]

The mean of a bivariate normal distribution with correlation

:

Needs["MultivariateStatistics`"]

The variances of each dimension:

Needs["MultivariateStatistics`"]

Probability density function:

Generate a set of pseudorandom vectors that follow a trivariate normal distribution:

Equal probability contours for a bivariate normal distribution:

The probability density function integrates to unity:

MultinormalDistribution is not defined when

is not a vector of real numbers:

MultinormalDistribution is not defined when the dimensions of

and

are not consistent:

MultinormalDistribution is not defined when

is not symmetric and positive definite:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful: