moments
Central moments
Description
It calculates up to fourth central moments (or moments about the mean), and the skewness and kurtosis coefficients using an online algorithm.
Usage
Arguments
| Argument | Description |
|---|---|
x |
a numeric vector containing the sample observations. |
Details
The \(k\) -th central moment is defined as
\[m_k = \frac{1}{n}\sum_{i=1}^n (x_i - \overline{x})^k.\]
In particular, the second central moment is the variance of the sample. The sample skewness and kurtosis are defined, respectively, as
\[b_1 = \frac{m_3}{s^3}, \qquad b_2 = \frac{m_4}{s^4} - 3,\]
where \(s\) denotes de standard deviation.
Value
A list containing second , third and fourth central moments,
and skewness and kurtosis coefficients.
Seealso
var .
References
Spicer, C.C. (1972). Algorithm AS 52: Calculation of power sums of deviations about the mean. Applied Statistics 21 , 226-227.