Definition:Kurtosis

Definition
Let $X$ be a random variable with mean $\mu$ and standard deviation $\sigma$.

Then the kurtosis of $X$, usually denoted $\alpha_4$, is defined as:


 * $\alpha_4 = \expect {\paren {\dfrac {X - \mu} \sigma}^4}$

where $\expect X$ denotes the expectation of $X$.

That is, the kurtosis of $X$ is the fourth standardized moment of $X$.

Also see

 * Definition:Standardized Moment