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The graph of a Gaussian is a characteristic symmetric "bell curve" shape. ... Gaussian functions are widely used in statistics to describe the normal distributions, ...
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 ...
A graph of the function () = and the area between it and the -axis, (i.e. the entire real line) which is equal to . The Gaussian integral , also known as the Euler–Poisson integral , is the integral of the Gaussian function f ( x ) = e − x 2 {\displaystyle f(x)=e^{-x^{2}}} over the entire real line.
The Gaussian function is the archetypal example of a bell shaped function. A bell-shaped function or simply 'bell curve' is a mathematical function having a characteristic "bell"-shaped curve. These functions are typically continuous or smooth, asymptotically approach zero for large negative/positive x, and have a single, unimodal maximum at ...
In statistics, the Q-function is the tail distribution function of the standard normal distribution. [ 1 ] [ 2 ] In other words, Q ( x ) {\displaystyle Q(x)} is the probability that a normal (Gaussian) random variable will obtain a value larger than x {\displaystyle x} standard deviations.
Cobweb plot of the Gauss map for = and =.This shows an 8-cycle. In mathematics, the Gauss map (also known as Gaussian map [1] or mouse map), is a nonlinear iterated map of the reals into a real interval given by the Gaussian function:
Copula, for the definition of the Gaussian or normal copula model. Multivariate t-distribution, which is another widely used spherically symmetric multivariate distribution. Multivariate stable distribution extension of the multivariate normal distribution, when the index (exponent in the characteristic function) is between zero and two.
The graph of the bump function ... This function can be interpreted as the Gaussian function ... Bump functions defined in terms of a function : ...