Zipf extensions and their applications for modeling the degree sequences of real networks

• Autores: Ariel Duarte López
• Directores de la Tesis: Marta Pérez Casany (dir. tes.)
• Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2021
• Idioma: español
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• Resumen

  • The Zipf distribution, also known as discrete Pareto distribution, attracts considerable attention because it helps describe skewed data from many natural as well as man-made systems. Under the Zipf distribution, the frequency of a given value is a power function of its size. Consequently, when plotting the frequencies versus the size in log-log scale for data following this distribution, one obtains a straight line. Nevertheless, for many data sets the linearity is only observed in the tail and when this happens, the Zipf is only adjusted for values larger than a given threshold. This procedure implies a loss of information, and unless one is only interested in the tail of the distribution, the need to have access to more flexible alternatives distributions is evidenced.

    The work conducted in this thesis revolves around 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. In order to analyze the performance of these models, we have fitted 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. To facilitate the use of the models presented, they have been implemented in the zipfextR package available in the Comprehensive R Archive Network.