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.

Notation

The kurtosis of $X$ is usually denoted $\alpha_4$.

Some sources denote the kurtosis by the symbol $\Beta_2$ or $\beta_2$.

Also see

• Equivalence of Definitions of Kurtosis

Sources

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