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}\sum\limits_{i=1}^n\sum\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}\sum\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, |
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 0.5-772 Index]