Definition:Excess Kurtosis

Definition

Excess kurtosis is defined as the difference between the kurtosis of a particular probability distribution and that of the normal distribution.

Let $X$ be a random variable with kurtosis $\alpha_4$.

By Kurtosis of Normal Distribution, the kurtosis of a normal distribution is equal to $3$.

So the excess kurtosis of $X$, usually denoted $\gamma_2$, is given by:

$\gamma_2 = \alpha_4 - 3$

Also known as

Some sources give this as kurtosis excess.

Also see

• Definition:Kurtosis

Sources

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