Generate random numbers distributed by Zipf

Question

The Zipf probability distribution is often used to model file size distribution or item access distributions on items in P2P systems. e.g. "Web Caching and Zip like Distribution Evidence and Implications", but neither Boost or the GSL (Gnu Scientific Library) provide an implementation to generate random numbers using this distribution. I have not found a (trustworthy) implementation using the common search engines.

How can random numbers that are distributed according to the Zipf distribution by using a U(0,1) random generator, e.g. the Mersenne twister?

Answer 1

zipfR is a free and open source library implemented with R. VGAM is another R package that also implements Zipf.

It's also worth noting that the Gnu Scientific Library has an implementation of the Pareto distribution which is effectively the continuous analogue of the discrete Zipf distribution.

Also, the Zeta distribution is equivalent to Zipf for infinite N. The GSL has an implementation of the Riemann zeta function, so you could use that to construct the distribution yourself.

Answer 2

numpy.random.zipf generates Zipf samples using python.

Answer 3

numpy.random.zipf can only support alpha greater than 1. I need alpha less than 1. Am I missing something?