Definition:Kurtosis/Coefficient

Definition

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

The coefficient of kurtosis of $X$ is the coefficient:

$\gamma_2 = \dfrac {\mu_4} { {\mu_2}^2} - 3$

where $\mu_i$ denotes the $i$th central moment of $X$.

Also see

• Results about kurtosis can be found here.

Linguistic Note

The word kurtosis derives from the Greek κυρτός (kyrtos or kurtos), meaning curved or arching.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): coefficient of kurtosis
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): kurtosis
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): coefficient of kurtosis
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): kurtosis