Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Skewness ▷ Sample skewness

Definition: Let $x = \left\lbrace x_1, \ldots, x_n \right\rbrace$ be a sample from a random variable $X$. Then, the sample skewness of $x$ is given by

\[\label{eq:skew-samp} \hat{s} = \frac{\frac{1}{n}\sum_{i=1}^n (x_i-\bar{x})^3}{\left[\frac{1}{n}\sum_{i=1}^n(x_i-\bar{x})^2\right]^{3/2}} \; ,\]

where $\bar{x}$ is the sample mean.

 
Sources:
  • Joanes, D. N. and Gill, C. A. (1998): "Comparing measures of sample skewness and kurtosis"; in: The Statistician, vol. 47, part 1, pp. 183-189; URL: https://www.jstor.org/stable/2988433.

Metadata: ID: D190 | shortcut: skew-samp | author: tomfaulkenberry | date: 2023-10-30, 12:00.