| kurtosis {fastmatrix} | R Documentation |
Functions to compute measures of multivariate skewness (b_1) and kurtosis (b_2) proposed by Mardia (1970),
b_1 = \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_2 = \frac{1}{n}∑\limits_{i=1}^n ((\bold{x}_i - \overline{\bold{x}})^T \bold{S}^{-1}(\bold{x}_j - \overline{\bold{x}}))^2.
kurtosis(x) skewness(x)
x |
vector or matrix of data with, say, p columns. |
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.
setosa <- iris[1:50,1:4] kurtosis(setosa) skewness(setosa)