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:
“What strikes many twin researchers now is not how much identical twins are alike, but rather how different they are, given the same genetic makeup....Multiples don’t walk around in lockstep, talking in unison, thinking identical thoughts. The bond for normal twins, whether they are identical or fraternal, is based on how they, as individuals who are keenly aware of the differences between them, learn to relate to one another.”
—Pamela Patrick Novotny (20th century)
“My topic for Army reunions ... this summer: How to prepare for war in time of peace. Not by fortifications, by navies, or by standing armies. But by policies which will add to the happiness and the comfort of all our people and which will tend to the distribution of intelligence [and] wealth equally among all. Our strength is a contented and intelligent community.”
—Rutherford Birchard Hayes (1822–1893)