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Encyclopedia > Matrix normal distribution

The matrix normal distribution is a probability distribution that is a generalization of the normal distribution. The probability density function for the random matrix X(N x P) that follows the matrix normal distribution has the form Results from FactBites:

 Normal distribution - Wikipedia, the free encyclopedia (4059 words) The normal distribution was first introduced by de Moivre in an article in 1733 (reprinted in the second edition of his The Doctrine of Chances, 1738) in the context of approximating certain binomial distributions for large n. In that case, the assumption of normality is not justified, and it is the logarithm of the variable of interest that is normally distributed. The derivation of the maximum-likelihood estimator of the covariance matrix of a multivariate normal distribution is perhaps surprisingly subtle and elegant.
 Multivariate normal distribution - Wikipedia, the free encyclopedia (799 words) In probability theory and statistics, a multivariate normal distribution, also sometimes called a multivariate Gaussian distribution (in honor of Carl Friedrich Gauss, who was not the first to write about the normal distribution) is a specific probability distribution. The cumulative distribution function (cdf) F ( x) is defined as the probability that all values in a random vector X are less than or equal to the corresponding values in vector x. Two random variables that are normally distributed may fail to be jointly normally distributed, i.e., the vector whose components they are may fail to have a multivariate normal distribution.
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