A set of statistical metrics, characterizing the deviation of a given numerical dataset
x = \{ x_1, \, x_2, \, x_3 , ... x_N \} from its Mean Value
\mu(x) :
\bar \mu_n = \frac{\mu_n}{\sigma^n}, \ \ n \geq 3 |
where
N | |
E | |
\mu_n | n-order of central momentum |
\sigma |
The concept makes sense only for the central momentums of higher oder than
n \geq 3, since lower order central momentums
\bar \mu_0 \equiv 1/\sigma,
\bar \mu_1 \equiv 0,
\bar \mu_2 \equiv 1 are trivial and do not carry additional information on dataset distribution.
The most popular application is the 3-rd order standardized central momentum \mu_3 = \bar \mu_3 \cdot \sigma^3, which is called skewness and characterizes asymmetry of the dataset distribution.
See also
Formal science / Mathematics / Statistics / Statistical Metric / Central momentum