# Statistics / Probability - Gaussian function ( )

In statistics and probability theory, Gaussian functions appear as the density function of the normal distribution, which is a limiting probability distribution of complicated sums, according to the central limit theorem.

## Syntax

### Simplified

A Gaussian function is generally simplified by:

$$f(x)=e^{\displaystyle -x^2}$$

### Detailled

A Gaussian is a function of the form:

$$f(x)=ae^{-{\frac {\displaystyle(x-b)^{2}}{\displaystyle 2c^{2}}}}$$ where:

• The variable a defines the position of its mode (ie peak) on the y axis.
• The variable b defines the position of its mode (ie peak) on the x axis.
• The variable c defines the spread

## Play

// the position of the mode (ie peak) on the ''y'' axis.
var a = 0.9;
// The position of the modeon the x axis (ie the position of the pick on the x axis)
var b = -2;
var c = 2;

// The gaussian function
var exponent = (x) => Math.pow((x-b),2) / (2*Math.pow(c,2))
var func = (x) =>  a * Math.pow( Math.E ,  -exponent(x) );

// The graph
var graph = new world.func(func)
.setTitle("A gaussian function where a="+a+", b="+b+", c="+c)
.render();


## Documentation / Reference

Discover More
Statistics - (Normal|Gaussian) Distribution - Bell Curve

A normal distribution is one of underlying assumptions of a lot of statistical procedures. In nature, every outcome that depends on the sum of many independent events will approximate the Gaussian distribution...
Statistics - Central limit theorem (CLT)

The Central_limit_theoremcentral limit theorem (CLT) is a probability theorem (unofficial sovereign) It establishes that when: random variables (independent) (estimate of a random process) are added...