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 = <\mu_n> = \frac{\mu_n}{\sigma^n} E[ ( x - \mu)^n ] = \frac{1}{N} \sum_{i=1}^N (x_i - \mu)^n |
where
N | |
E | |
n | order of central momentum |
\sigma |
The common assumption is that zero-th central momentum is unit-value: \mu_0 \equiv 1.
By definition the first central momentum is always zero: \mu_1 \equiv 0.
The second central momentum (μ2) is also called variance \mu_2 = \sigma^2, where \sigma is standard deviation.
The third central momentum is characterizing asymmetry of the variance \mu_3 = \bar \mu_3 \cdot \sigma^3, where \bar \mu_3 is skewness.
See also
Formal science / Mathematics / Statistics / Statistical Metric