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 Resource. https://mathworld.wolfram.com/FunctionCentroid.html
Subject classifications
