# moments: Central moments In fastmatrix: Fast Computation of some Matrices Useful in Statistics

## Description

It calculates up to fourth central moments (or moments about the mean), and the skewness and kurtosis coefficients using an online algorithm.

## Usage

 1 moments(x) 

## Arguments

 x a numeric vector containing the sample observations.

## Details

The k-th central moment is defined as

m_k = \frac{1}{n}∑_{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.

## References

Spicer, C.C. (1972). Algorithm AS 52: Calculation of power sums of deviations about the mean. Applied Statistics 21, 226-227.

var.
 1 2 3 4 set.seed(149) x <- rnorm(1000) z <- moments(x) z