moments: Central moments

In fastmatrix: Fast Computation of some Matrices Useful in Statistics

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

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}\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}{m_2^{3/2}}, \qquad b_2 = \frac{m_4}{m_2^2}.

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.

See Also

var.

Examples

set.seed(149)
x <- rnorm(1000)
z <- moments(x)
z

fastmatrix documentation built on Oct. 12, 2023, 5:14 p.m.