MultivariateStatistics`
MultivariateStatistics`

MultinormalDistribution

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

MultinormalDistribution[μ,Σ]

represents a multivariate normal (Gaussian) distribution with mean vector μ and covariance matrix Σ.

Details

• 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-μ).Σ-1.(x-μ)/2.
• The mean μ can be any vector of real numbers, and Σ can be any symmetric positive definite p×p matrix with p=Length[μ].
• MultinormalDistribution can be used with such functions as Mean, CDF, and RandomReal.

Examples

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Basic Examples(3)

 In:= The mean of a bivariate normal distribution with correlation ρ:

 In:= Out= In:= The variances of each dimension:

 In:= Out= In:= Probability density function:

 In:= Out= In:= Out= 