OBSOLETE MULTIVARIATE STATISTICS PACKAGE SYMBOL

MultinormalDistribution

As of Version 8, MultinormalDistribution is part of the built-in Mathematica kernel.

represents a multivariate normal (Gaussian) distribution with mean vector

and covariance matrix

.

The probability density for vector x in a multivariate normal distribution is proportional to .

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

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

:

Out[2]=

Needs["MultivariateStatistics`"]

The variances of each dimension:

Out[2]=

Needs["MultivariateStatistics`"]

Probability density function:

Out[2]=

Out[3]=

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:

is not defined when

is not a vector of real numbers:

is not defined when the dimensions of

and

are not consistent:

is not defined when

is not symmetric and positive definite:

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