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In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.The general form of its probability density function is [2] [3] = ().
It is ubiquitous in nature and statistics due to the central limit theorem: every variable that can be modelled as a sum of many small independent, identically distributed variables with finite mean and variance is approximately normal. The normal-exponential-gamma distribution; The normal-inverse Gaussian distribution
In statistics and probability theory, Gaussian functions appear as the density function of the normal distribution, which is a limiting probability distribution of complicated sums, according to the central limit theorem.
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.
It is possible to have variables X and Y which are individually normally distributed, but have a more complicated joint distribution. In that instance, X + Y may of course have a complicated, non-normal distribution. In some cases, this situation can be treated using copulas.
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence ... (Gaussian distribution), ...
Equivalently, it is generated by = (+) /, where is an matrix with IID samples from the standard normal distribution. The Gaussian symplectic ensemble is described by the Gaussian measure with density on the space of n × n Hermitian quaternionic matrices, e.g. symmetric square matrices composed of quaternions, H = (H ij) n
In statistics, the Q-function is the tail distribution function of the standard normal distribution. [1] [2] In other words, () is the probability that a normal (Gaussian) random variable will obtain a value larger than standard deviations.