\begin{definition}[Definition:Excess Kurtosis]
'''Excess kurtosis''' is defined as the difference between the kurtosis of a particular probability distribution and that of the Gaussian distribution.
Let $X$ be a random variable with kurtosis $\alpha_4$. 
By Kurtosis of Gaussian Distribution, the kurtosis of a Gaussian distribution is equal to $3$. 
So the '''excess kurtosis''' of $X$, usually denoted $\gamma_2$, is given by: 
:$\gamma_2 = \alpha_4 - 3$
\end{definition}