Definition 1.7.3. Kurtosis.
For population data, the Kurtosis of \(x_1, x_2, ..., x_n\) is given by
\begin{equation*}
\gamma_2 = \frac{1}{\sigma^4} \frac{\sum_{k=1}^n ( x_k-\mu )^4}{n}.
\end{equation*}
For sample data, the Kurtosis of \(x_1, x_2, ..., x_n\) is given by
\begin{equation*}
g_2 = \frac{1}{s^4} \frac{\sum_{k=1}^n ( x_k-\overline{x} )^4}{n-1}.
\end{equation*}