R: Mardia's multivariate skewness and kurtosis coefficients

kurtosis {fastmatrix} | R Documentation

## Mardia's multivariate skewness and kurtosis coefficients

### Description

Functions to compute measures of multivariate skewness (b_{1p}) and kurtosis (b_{2p}) proposed by Mardia (1970),

b_{1p} = \frac{1}{n^2}∑\limits_{i=1}^n∑\limits_{j=1}^n ((\bold{x}_i - \overline{\bold{x}})^T\bold{S}^{-1}(\bold{x}_j - \overline{\bold{x}}))^3,

and

b_{2p} = \frac{1}{n}∑\limits_{i=1}^n ((\bold{x}_i - \overline{\bold{x}})^T \bold{S}^{-1}(\bold{x}_j - \overline{\bold{x}}))^2.

### Usage

    kurtosis(x)

    skewness(x)

### Arguments

`x` | matrix of data with, say, p columns.

### References

Mardia, K.V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika 57, 519-530.

Mardia, K.V., Zemroch, P.J. (1975). Algorithm AS 84: Measures of multivariate skewness and kurtosis. Applied Statistics 24, 262-265.

### Examples

    setosa <- iris[1:50,1:4]
    kurtosis(setosa)
    skewness(setosa)

[Package fastmatrix version 0.4-1 Index]