MSkew {mnt} | R Documentation |
This function computes the classical invariant measure of multivariate sample skewness due to Mardia (1970).
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}\sum_{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,\ldots,X_n
. To ensure that the computation works properly
n \ge 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.
MSkew(MASS::mvrnorm(50,c(0,1),diag(1,2)))