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:
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).