Gaussian Function
Gaussian Function
\[y = ae^{-\frac{(x-b)^2}{2c^2}}\]
Variables
y = function value
a = peak amplitude
b = center position
c = standard deviation parameter
x = independent variable
Description
What is this formula?
This formula represents a Gaussian function, also known as a bell curve. It describes symmetric distributions centered around a mean value.
When to use it
Use this formula when modeling normal distributions, signal profiles or natural statistical variations.
Example
For:
a=10
b=0
c=2
x=1
y=10*(℮^(-((1²)/(2*2²))))
y=10*(℮^(-0.125))
y≈8.82
Applications
Statistics
Signal processing
Optics
Probability theory
Data analysis
Machine learning
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