pcKbSkew {KbMvtSkew} | R Documentation |
Compute Principal-component-based Khattree-Bahuguna's Multivariate Skewness.
pcKbSkew(x, cor = FALSE)
x |
a matrix of original scale observations. |
cor |
a logical value indicating whether the calculation should use the correlation matrix ( |
Let \mathbf{X} = X_1, \ldots, X_p
be a p
-dimensional multivariate random vector. We compute the sample skewness for p
principal components of \mathbf{X}
respectively by the sample Khattree-Bahuguna's univariate skewness formula (see details of kbSkew
that follows). Let \eta_1, \eta_2, \ldots, \eta_p
be the p
univariate skewnesses for p
principal components. Principal-component-based Khattree-Bahuguna's multivariate skewness for a sample is then defined as
\eta = \sum_{i=1}^{p} \eta_i.
Clearly, 0 \le \eta \le \frac{p}{2}
.
pcKbSkew
gives the sample principal-component-based Khattree-Bahuguna's multivairate skewness.
Khattree, R. and Bahuguna, M. (2019). An alternative data analytic approach to measure the univariate and multivariate skewness. International Journal of Data Science and Analytics, Vol. 7, No. 1, 1-16.
kbSkew
for Khattree-Bahuguna's univariate skewness.
# Compute principal-component-based Khattree-Bahuguna's multivairate skewness
data(OlymWomen)
pcKbSkew(OlymWomen[, c("m800","m1500","m3000","marathon")])