  The Zipf distribution also known as scale-free distribution or discrete
Pareto distribution, is the particular case of Power Law distribution with
support the strictly positive integers. It is a one-parameter distribution with
a linear behaviour in the log-log scale. In this paper the Zipf distribution is
generalized by means of the Marshall-Olkin transformation. The new model has
more flexibility to adjust the probabilities of the first positive integer
numbers while keeping the linearity of the tail probabilities. The main
properties of the new model are presented, and several data sets are analyzed
in order to show the gain obtained by using the generalized model.
