In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution, is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One possible definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. However, its importance derives mainly from the multivariate central limit theorem. The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables each of which clusters around a mean value.
Read more about Multivariate Normal Distribution: Notation and Parametrization, Definition, Conditional Distributions, Marginal Distributions, Affine Transformation, Geometric Interpretation, Estimation of Parameters, Bayesian Inference, Multivariate Normality Tests, Drawing Values From The Distribution
Famous quotes containing the words normal and/or distribution:
“A few ideas seem to be agreed upon. Help none but those who help themselves. Educate only at schools which provide in some form for industrial education. These two points should be insisted upon. Let the normal instruction be that men must earn their own living, and that by the labor of their hands as far as may be. This is the gospel of salvation for the colored man. Let the labor not be servile, but in manly occupations like that of the carpenter, the farmer, and the blacksmith.”
—Rutherford Birchard Hayes (1822–1893)
“In this distribution of functions, the scholar is the delegated intellect. In the right state, he is, Man Thinking. In the degenerate state, when the victim of society, he tends to become a mere thinker, or, still worse, the parrot of other men’s thinking.”
—Ralph Waldo Emerson (1803–1882)