| PearsonSkew {KbMvtSkew} | R Documentation |
Pearson's coefficient of skewness
Description
Compute Pearson's coefficient of skewness.
Usage
PearsonSkew(x)
Arguments
x |
a vector of original observations. |
Details
Pearson's coefficient of skewness is defined as
\gamma_1 = \frac{E[(X - \mu)^3]}{(\sigma^3)}
where \mu = E(X) and \sigma^2 = E[(X - \mu)^2]. The sample version based on a random sample x_1,x_2,\ldots,x_n is defined as
\hat{\gamma_1} = \frac{\sum_{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.
Value
PearsonSkew gives the sample Pearson's univariate skewness.
References
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.
Examples
# 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)