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The graph of a Gaussian is a characteristic symmetric "bell curve" shape. ... For the general form of the equation the coefficient A is the height of the peak and ...
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 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 ...
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.
For a Gaussian process, all sets of values have a multidimensional Gaussian distribution. Analogously, X ( t ) {\displaystyle X(t)} is a Student t process on an interval I = [ a , b ] {\displaystyle I=[a,b]} if the correspondent values of the process X ( t 1 ) , …
The equation above reduces to that of the univariate normal distribution if is a matrix (i.e., a single real number). The circularly symmetric version of the complex normal distribution has a slightly different form.
In wireless communication, "the local-mean power expressed in logarithmic values, such as dB or neper, has a normal (i.e., Gaussian) distribution." [90] Also, the random obstruction of radio signals due to large buildings and hills, called shadowing, is often modeled as a log-normal distribution.
Full width at half maximum. In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value.