Gaussian function
lastmod 2018-08-17created 2014-11-026 edits
Red is the standard normal distribution
In mathematics, a Gaussian function is a function of the following form.
Gaussian_function.png
- e=2.718281828.... (Euler’s number)
- a: maximum value of the curve
- b: x coordinate at which the maximum occurs
- c: determines the width of the curve
Here a (> 0), b, c are real constants. The function is named after Carl Friedrich Gauss.
The graph of a Gaussian function is a symmetric bell-shaped curve that decreases rapidly toward the +/- limits. The parameter a is the height of the curve's peak, and b is the position of the center of the peak. c determines the width of the bell.
The Gaussian function is the derivative of the error function. The Gaussian function is also the density function of the normal distribution, and it is used in many other ways in the natural sciences and statistics.
See also
- Normal distribution
- Probability density function (PDF)
- Cumulative distribution function
- Gaussian blur (Image Processing)