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All these extensions are also called normal or Gaussian laws, so a certain ambiguity in names exists. The multivariate normal distribution describes the Gaussian law in the k-dimensional Euclidean space. A vector X ∈ R k is multivariate-normally distributed if any linear combination of its components Σ k j=1 a j X j has a (univariate) normal ...
The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables. It is a special case of the Gamma distribution, and it is used in goodness-of-fit tests in statistics. The inverse-chi-squared distribution; The noncentral chi-squared distribution; The scaled inverse chi-squared distribution; The Dagum ...
In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional normal distribution to higher dimensions.
This is the characteristic function of the normal distribution with expected value ... It can be shown that the Fourier transform of a Gaussian, () = (; ...
The generalized normal distribution (GND) or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line. Both families add a shape parameter to the normal distribution. To distinguish the two families, they are referred to below as "symmetric" and "asymmetric"; however ...
In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random ...
The probability density function for the random matrix X (n × p) that follows the matrix normal distribution , (,,) has the form: (,,) = ([() ()]) / | | / | | /where denotes trace and M is n × p, U is n × n and V is p × p, and the density is understood as the probability density function with respect to the standard Lebesgue measure in , i.e.: the measure corresponding to integration ...
In mathematical physics and probability and statistics, the Gaussian q-distribution is a family of probability distributions that includes, as limiting cases, the uniform distribution and the normal (Gaussian) distribution. It was introduced by Diaz and Teruel. [clarification needed] It is a q-analog of the Gaussian or normal distribution.