If the probability distribution of X is Gaussian^ (aka Normal) with mean (µ or mu) and variance sigma squared (ó^{2} or sigma2) we write X ~ N(µ, ó^{2}). {ed, using ó as the greek letter sigma}. µ gives us the center of the normal bell curve, ó is the standard deviation^ or width from the center of the curve to the inflection point^ where the slope of the curve changes from concave to convex. ó^{2} is the variance.
In the figure here, the red line is the Normal distribution.
Another way of calculating this is:
ó^{2}=o^2
a = 1/sqrt(2 * Pi * ó^{2})
g(x) = a * exp(0.5 * ( (xµ)^2 / ó^{2}) )
Where ó^{2} is the variance which controls the width of the peak, µ is the "expected value" or position of the center of the peak, and a is the height of the peak. Setting a to 1/sqrt(2* Pi * ó^{2}) makes the integral of the curve exactly 1, so the area under the curve is a single unit.
Gausian functions are often used as kernels in Support Vector Machines, or in Anomaly Detection. They are also used in Kalman Filters for localization
See also:
file: /Techref/method/math/gaussian.htm, 2KB, , updated: 2017/6/29 16:11, local time: 2022/1/18 08:40,

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