The Zipf–Poisson-stopped-sum distribution with an application for modeling the degree sequence of social networks

Under the Zipf Distribution, the frequency of a value is a power function of its size. Thus, when plotting frequencies versus size in log–log scale of data following that distribution, one obtains a straight line. The Zipf has been assumed to be appropriate for modeling highly skewed data from many different areas. Nevertheless, for many real data sets, the linearity is observed only in the tail; thus, the Zipf is fitted only for values larger than a given threshold and, consequently, there is a loss of information. The Zipf–Poisson-stopped-sum distribution is introduced as a more flexible alternative. It is proven that in log–log scale allows for top-concavity, maintaining the linearity in the tail. Consequently, the distribution fits properly many data sets in their entire range. To prove the suitability of our model 16 network degree sequences describing the interaction between members of a given platform have been fitted. The results have been compared with the fits obtained through other bi-parametric distributions.