Definition:Skewness
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Definition
Skewness is a measure of the asymmetry of a probability distribution about its mean.
Let $X$ be a random variable with mean $\mu$ and standard deviation $\sigma$.
Then the skewness of $X$, usually denoted $\gamma_1$, is defined as:
- $\gamma_1 = \expect {\paren {\dfrac {X - \mu} \sigma}^3}$
where $\expect X$ denotes the expectation of $X$.
Coefficient of Skewness
Let $X$ be a random variable with mean $\mu$ and standard deviation $\sigma$.
The coefficient of skewness of $X$ is the coefficient:
- $\gamma_1 = \expect {\paren {\dfrac {X - \mu} \sigma}^3}$
where $\mu_i$ denotes the $i$th central moment of $X$.
Also see
- Results about skewness can be found here.
Sources
- Weisstein, Eric W. "Skewness." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Skewness.html