Definition:Kurtosis/Definition 1

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

The kurtosis of $X$ is a measure of the concentration of $X$ about its expectation.

The kurtosis of $X$ is the fourth standardized moment of $X$:


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

where $\expect {\, \cdot \,}$ denotes expectation.

Also see

 * Equivalence of Definitions of Kurtosis