Kurtosis

Definition

Pearson’s Kurtosis

The kurtosis is the fourth standardized moment, defined as $\mathrm{Kurt}(X)=\frac{E[(X-\mu {)}^4]}{(E[(X-\mu {)}^2]{)}^2}=\frac{{\mu }_4}{{\mu }_2^2}$ where ${\mu }_i$ is the $i$-th Central Moment

Excess Kurtosis

The excess kurtosis is defined as kurtosis minus 3

Facts

For any random variable $X$, the excess kurtosis is equal to or greater than $-2$