Definition:Kurtosis/Definition 2

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 defined as:

$\alpha_4 = \dfrac {\mu_4} {\paren {\mu_2}^2}$

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

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

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): kurtosis
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): kurtosis
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): kurtosis

• Weisstein, Eric W. "Kurtosis." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Kurtosis.html