KbMvtSkew (version 1.0.2)

kbSkew: Khattree-Bahuguna's Univariate Skewness

Description

Compute Khattree-Bahuguna's Univariate Skewness.

Usage

kbSkew(x)

Arguments

x

a vector of original observations.

Value

kbSkew gives the Khattree-Bahuguna's univariate skewness of the data.

Details

Given a univariate random sample of size \(n\) consist of observations \(x_1, x_2, \ldots, x_n\), let \(x_{(1)} \le x_{(2)} \le \cdots \le x_{(n)}\) be the order statistics of \(x_1, x_2, \ldots, x_n\) after being centered by their mean. Define $$y_ i = \frac{x_{(i)} + x_{(n - i + 1)}}{2}$$ and $$w_ i = \frac{x_{(i)} - x_{(n - i + 1)}}{2}$$ The sample Khattree-Bahuguna's univariate skewness is defined as $$\hat{\delta} = \frac{\sum y_i^2}{\sum y_i^2 + \sum w_i^2}.$$ It can be shown that \(0 \le \hat{\delta} \le \frac{1}{2}\). Values close to zero indicate, low skewness while those close to \(\frac{1}{2}\) indicate the presence of high degree of 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.

Examples

# NOT RUN {
# Compute Khattree-Bahuguna's univariate skewness

set.seed(2019)
x <- rnorm(1000) # Normal Distribution
kbSkew(x)

set.seed(2019)
y <- rlnorm(1000, meanlog = 1, sdlog = 0.25) # Log-normal Distribution
kbSkew(y)

# }