Multivariate Skewness and Kurtosis

Source: R/moments.R

Multivariate Skewness and Kurtosis

mardia(X)

Arguments

X

Matrix or data frame.

Value

Returns a vector with the following elements

b1

Estimate of multivariate skewness \(\left( b_{1, k} \right)\) .

b1.chisq

chi-square statistic \(\left( \frac{nb_{1, k}}{6} \right)\) .

b1.df

Degrees of freedom \(\left( \frac{k(k + 1)(k + 2)}{6} \right)\) .

b1.p

p-value associated with the chi-square statistic.

b2

Estimate of multivariate kurtosis \(\left( b_{2, k} \right)\) .

b2.z

z-statistic \(\left( \frac{b_{2, k} - k \left( k + 2 \right)}{\sqrt{\frac{8 k \left( k + 2 \right)}{n}}} \right)\) .

b2.p

p-value associated with the z-statistic.

Examples

set.seed(42)
n <- 100
mu <- c(0, 0, 0)
Sigma <- matrix(
  data = c(1, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 1),
  ncol = 3
)
X <- MASS::mvrnorm(n = n, mu = mu, Sigma = Sigma)
mardia(X)
#>                 b1           b1.chisq      b1.correction b1.chisq.corrected 
#>        1.510158866       25.169314434        1.030152993       25.928244596 
#>              b1.df               b1.p     b1.p.corrected                 b2 
#>       10.000000000        0.005033647        0.003837901       15.907980187 
#>               b2.z               b2.p 
#>        0.828868717        0.407178699