PearsonSkew: Pearson's coefficient of skewness
In KbMvtSkew: Khattree-Bahuguna's Univariate and Multivariate Skewness

Description Usage Arguments Details Value References Examples

View source: R/KbSkewness.R

Compute Pearson's coefficient of skewness.

1	PearsonSkew(x)

`x`	a vector of original observations.

Pearson's coefficient of skewness is defined as

γ_1 = \frac{E[(X - μ)^3]}{(σ^3)}

where μ = E(X) and σ^2 = E[(X - μ)^2]. The sample version based on a random sample x_1,x_2,…,x_n is defined as

\hat{γ_1} = \frac{∑_{i=1}^n (x_i - \bar{x})^3}{n s^3}

where \bar{x} is the sample mean and s is the sample standard deviation of the data, respectively.

PearsonSkew gives the sample Pearson's univariate skewness.

Pearson, K. (1894). Contributions to the mathematical theory of evolution. Philos. Trans. R. Soc. Lond. A 185, 71-110.

Pearson, K. (1895). Contributions to the mathematical theory of evolution II: skew variation in homogeneous material. Philos. Trans. R. Soc. Lond. A 86, 343-414.

# Compute Pearson's univariate skewness

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

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