Centroid (Function)

By analogy with the Geometric Centroid, the centroid of an arbitrary function $f(x)$ is defined as

$$\left\langle{x}\right\rangle{}={\int_{-\infty}^\infty xf(x)\,dx\over\int_{-\infty}^\infty f(x)\,dx}.$$

References

Bracewell, R. The Fourier Transform and Its Applications. New York: McGraw-Hill, pp. 139-140 and 156, 1965.