Zipf Extensions and Their Applications for Modeling the Degree Sequences of Real Networks

In this talk, I will present four bi-parametric extensions of the Zipf distribution. The first two belong to the class of Random Stopped Extreme distributions. The third extension is the result of applying the concept of Poisson-Stopped-Sum to the Zipf distribution and, the last one is obtained by including an additional parameter to the probability generating function of the Zipf. An interesting characteristic of three of the models presented is that they allow for a parameter interpretation that gives some insights about the mechanism that generates the data. Also, I analyze the performance of these models when used to fit the degree sequences of real networks from different areas as: social networks, protein interaction networks, or collaboration networks. The fits obtained have been compared with those obtained with other bi-parametric models such as: the Zipf-Mandelbrot, the discrete Weibull, or the negative binomial.