MSkew: Mardias measure of multivariate sample skewness
In mnt: Affine Invariant Tests of Multivariate Normality

Description Usage Arguments Details Value References Examples

This function computes the classical invariant measure of multivariate sample skewness due to Mardia (1970).

1	MSkew(data)

data

a n x d matrix of d dimensional data vectors.

Multivariate sample skewness due to Mardia (1970) is defined by

b_{n,d}^{(1)}=\frac{1}{n^2}∑_{j,k=1}^n(Y_{n,j}^\top Y_{n,k})^3,

where Y_{n,j}=S_n^{-1/2}(X_j-\overline{X}_n), \overline{X}_n is the sample mean and S_n is the sample covariance matrix of the random vectors X_1,…,X_n. To ensure that the computation works properly n ≥ d+1 is needed. If that is not the case the function returns an error. Note that for d=1, we have a measure proportional to the squared sample skewness.

value of sample skewness in the sense of Mardia.

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

Henze, N. (2002), Invariant tests for multivariate normality: a critical review, Statistical Papers, 43:467–506.