# Zipf Distribution

Posted by Beetle B. on Tue 06 June 2017

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).