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 * `

`g(x) = a * exp(-0.5 * ( (x-`µ`)^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:

- https://www.youtube.com/watch?v=C_zFhWdM4ic How filters work, with box blur and gaussian blur as examples.
- https://en.wikipedia.org/wiki/Gaussian_function

file: /Techref/method/math/gaussian.htm, 2KB, , updated: 2017/6/29 17:11, local time: 2024/7/24 11:19, |

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