MKurt {mnt} | R Documentation |
This function computes the classical invariant measure of multivariate sample kurtosis due to Mardia (1970).
MKurt(data)
data |
a n x d matrix of d dimensional data vectors. |
Multivariate sample kurtosis due to Mardia (1970) is defined by
b_{n,d}^{(2)}=\frac{1}{n}\sum_{j=1}^n\|Y_{n,j}\|^4,
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.
value of sample kurtosis 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.
MKurt(MASS::mvrnorm(50,c(0,1),diag(1,2)))