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