KbMvtSkew (version 1.0.2)

pcKbSkew: 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.

Value

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

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, \(0 \le \eta \le \frac{p}{2}\).

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

# NOT RUN {
# Compute principal-component-based Khattree-Bahuguna's multivairate skewness

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

# }