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# MultinormalDistribution

 MultinormalDistributionrepresents a multivariate normal (Gaussian) distribution with mean vector and covariance matrix .
• The probability density for vector in a multivariate normal distribution is proportional to .
• The mean can be any vector of real numbers, and can be any symmetric positive definite × matrix with p=Length[].
Probability density function:
Cumulative distribution function:
Mean and variance:
Covariance:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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Covariance:
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 Scope   (6)
Generate a set of pseudorandom vectors that follow a bivariate normal distribution:
Visualize the sample using a histogram:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Goodness-of-fit test:
Skewness and kurtosis are constant vectors:
Correlation:
Hazard function:
Univariate marginals follow a NormalDistribution:
Multivariate marginals follow a multivariate normal distribution:
 Applications   (1)
Show a distribution function and its histogram in the same plot:
Compare the PDF to its histogram version:
Compare the CDF to its histogram version:
Equal probability contours for a bivariate normal distribution:
The multinormal distribution is closed under affine transformation:
For specific values:
Relationships to other distributions:
NormalDistribution is the univariate case of multinormal distribution:
BinormalDistribution is the two-dimensional case of multinormal distribution:
Multinormal distribution is the limit of MultivariateTDistribution as goes to :
Multinormal distribution is related to RiceDistribution:
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:
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