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 16:11, local time: 2024/3/1 06:02, |

©2024 These pages are served without commercial sponsorship. (No popup ads, etc...).Bandwidth abuse increases hosting cost forcing sponsorship or shutdown. This server aggressively defends against automated copying for any reason including offline viewing, duplication, etc... Please respect this requirement and DO NOT RIP THIS SITE. Questions?<A HREF="http://techref.massmind.org/techref/method/math/gaussian.htm"> Math Methods for Gaussian Distribution</A> |

Did you find what you needed? |

## Welcome to massmind.org! |

## Welcome to techref.massmind.org! |

.