Suppose you have a library with \(M\) items and you want to sort them by popularity.

The parameters are \(M\) and \(\alpha\). The domain is the numbers from 1 to \(M\). The pmf is:

\begin{equation*}
\frac{k^{-\alpha}}{Z}
\end{equation*}

where \(Z\) is the normalization constant.

The distribution gives the probability an item is borrowed from the library. \(k\) is the rank (sorted in descending order).