By analogy with the geometric centroid, the centroid of an arbitrary function 
is defined as
 |
(1)
|
where the integrals are taken over the domain of 
. For example, for the Gaussian
function 
,
the centroid is
 |
(2)
|
If 
is normalized so that
 |
(3)
|
then its centroid is equivalent to its mean.
See also
Geometric Centroid,
Mean,
Triangle Centroid
Explore with Wolfram|Alpha
References
Bracewell, R. The Fourier Transform and Its Applications, 3rd ed. New York: McGraw-Hill, pp. 139-140
and 156, 1999.Referenced on Wolfram|Alpha
Function Centroid
Cite this as:
Weisstein, Eric W. "Function Centroid."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FunctionCentroid.html
Subject classifications
