In this paper, we extend the Zipf distribution by means of the Randomly Stopped Extreme mechanism; we establish the conditions under which the maximum and minimum families of distributions intersect in the original family; and we demonstrate how to generate data from the extended family using any Zipf random number generator. We study in detail the particular cases of geometric and positive Poisson stopping distributions, showing that, in log-log scale, the extended models allow for top-concavity (top-convexity) while maintaining linearity in the tail. We prove the suitability of the models presented, by fitting the degree sequences in a collaboration and a protein-protein interaction networks. The proposed models not only give a good fit, but they also allow for extracting interesting insights related to the data generation mechanism.

在本文中，我们通过随机停止极值机制扩展了Zipf分布。我们确定了最大和最小分布族在原始族中相交的条件；并且我们演示了如何使用任何Zipf随机数生成器从扩展家族生成数据。我们详细研究了几何和正泊松停止分布的特殊情况，表明在对数对数尺度上，扩展模型允许顶部凹面（顶部凸面），同时保持尾部线性。通过在协作和蛋白质-蛋白质相互作用网络中拟合度序列，我们证明了所提出模型的适用性。提出的模型不仅非常适合，而且还可以提取与数据生成机制有关的有趣见解。