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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] = ().
The probability content of the multivariate normal in a quadratic domain defined by () = ′ + ′ + > (where is a matrix, is a vector, and is a scalar), which is relevant for Bayesian classification/decision theory using Gaussian discriminant analysis, is given by the generalized chi-squared distribution. [17]
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.
The normal distribution, also called the Gaussian or the bell curve. 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.
In reliability analysis, the log-normal distribution is often used to model times to repair a maintainable system. [95] In wireless communication, "the local-mean power expressed in logarithmic values, such as dB or neper, has a normal (i.e., Gaussian) distribution."
The Gaussian integral, ... This form is useful for calculating expectations of some continuous probability distributions related to the normal distribution, ...
The standard complex normal random variable or standard complex Gaussian random variable is a complex random variable whose real and imaginary parts are independent normally distributed random variables with mean zero and variance /. [3]: p. 494 [4]: pp. 501 Formally,
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 ...