@wikipedia
A set of statistical metrics, characterizing the average deviation of a given numerical the numerical values in the given dataset | LaTeX Math Inline |
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| body | --uriencoded--x = \%7B x_1, \, x_2, \, x_3 , ... x_N \%7D |
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from its Mean Value :
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\bar \mu_n = \frac{\mu_n}{\sigma^n}, E[ ( x - \mu)^n ] = \frac{1}{N} \sum_{i=1}^N (x_i - \mu)^n\ \ n \geq 3 |
where
The common assumption is that zero-th central momentum is unit-value: concept makes sense only for the central momentums of higher oder than
, since lower order central momentums | LaTeX Math Inline |
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| body | \bar \mu_0 \equiv 1/\sigma |
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.By definition the first central momentum is always zero: , .The second central momentum (μ2) is also called variance , | LaTeX Math Inline |
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| body | --uriencoded--\bar \mu_2 = \sigma%5e2 |
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, where is standard deviation. are trivial and do not carry additional information on dataset distribution.The most popular application is the 3-rd order standardized central momentum The third central momentum is characterizing asymmetry of the variance
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| body | --uriencoded--\mu_3 = \bar \mu_3 \cdot \sigma%5e3 |
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,
where is skewnesswhich is called skewness and characterizes asymmetry of the dataset distribution.
See also
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Formal science / Mathematics / Statistics / Statistical Metric Natural Science / System / Model Central momentum
