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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 :
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Needs["MultivariateStatistics`"]
The variances of each dimension:
In[2]:=
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Out[2]=
 
Needs["MultivariateStatistics`"]
Probability density function:
In[2]:=
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Out[2]=
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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: