# Multivariate Normal Distribution

Encyclopedia
Edited by: Published: 2010

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One of the most familiar distributions in statistics is the normal or Gaussian distribution. It has two parameters, corresponding to the first two moments (mean and variance). Once these parameters are known, the distribution is completely specified. The multivariate normal distribution is a generalization of the normal distribution and also has a prominent role in probability theory and statistics. Its parameters include not only the means and variances of the individual variables in a multivariate set but also the correlations between those variables. The success of the multivariate normal distribution is due to its mathematical tractability and to the multivariate central limit theorem, which states that the sampling distributions of many multivariate statistics are normal, regardless of the parent distribution. Thus, the multivariate normal distribution ...

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