MKurt {mnt}

Mardias measure of multivariate sample kurtosis

Description

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

Usage

MKurt(data)

Arguments

data

a n x d matrix of d dimensional data vectors.

Details

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

value of sample kurtosis in the sense of Mardia.

References

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.

Examples

MKurt(MASS::mvrnorm(50,c(0,1),diag(1,2)))