mnt (version 1.3)

MKurt: 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.

Value

value of sample kurtosis in the sense of Mardia.

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.

References

Mardia, K.V. (1970), Measures of multivariate skewness and kurtosis with applications, Biometrika, 57:519<U+2013>530.

Henze, N. (2002), Invariant tests for multivariate normality: a critical review, Statistical Papers, 43:467<U+2013>506.

Examples

# NOT RUN {
MKurt(MASS::mvrnorm(50,c(0,1),diag(1,2)))

# }