pcKbSkew {KbMvtSkew}

Principal-component-based Khattree-Bahuguna's Multivariate Skewness

Description

Compute Principal-component-based Khattree-Bahuguna's Multivariate Skewness.

Usage

pcKbSkew(x, cor = FALSE)

Arguments

x

a matrix of original scale observations.

cor

a logical value indicating whether the calculation should use the correlation matrix (cor = TRUE) or the covariance matrix (cor = FALSE). The default value is cor = FALSE.

Details

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}.

Value

pcKbSkew gives the sample principal-component-based Khattree-Bahuguna's multivairate skewness.

References

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.

See Also

kbSkew for Khattree-Bahuguna's univariate skewness.

Examples

# Compute principal-component-based Khattree-Bahuguna's multivairate skewness

data(OlymWomen)
pcKbSkew(OlymWomen[, c("m800","m1500","m3000","marathon")])