kbSkew: Khattree-Bahuguna's Univariate Skewness

In KbMvtSkew: Khattree-Bahuguna's Univariate and Multivariate Skewness

Description

Compute Khattree-Bahuguna's Univariate Skewness.

Usage

kbSkew(x)

Arguments

x	a vector of original observations.

Details

Given a univariate random sample of size n consist of observations x_1, x_2, …, x_n, let x_{(1)} ≤ x_{(2)} ≤ \cdots ≤ x_{(n)} be the order statistics of x_1, x_2, …, 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{δ} = \frac{∑ y_i^2}{∑ y_i^2 + ∑ w_i^2}.

It can be shown that 0 ≤ \hat{δ} ≤ \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.

Value

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

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

# 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)

KbMvtSkew documentation built on March 26, 2020, 7:44 p.m.