| kbSkew {KbMvtSkew} | R Documentation |
Khattree-Bahuguna's Univariate 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, \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.
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)