Scientists reinvent stochastic mechanisms leading to the emergence of a distribution discovered by H.A. Simon, in the context of the study of word frequencies occurring in a textbook. Simon distributions are heavy-tailed as a result of a reinforcement mechanism that produced them, related to the modern notion of preferential attachment. The Simon distribution is a particular case of a distribution recently introduced, itself extending the Sibuya distribution. We exhibit some of the remarkable statistical properties of such a family of distributions, in particular the one of being discrete self-decomposable. Using this and after placing this problem in context, additional stochastic processes where such distributions naturally arise are investigated, in particular a Markov chain model with catastrophes.

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关于导致与Yule-Simon相关的重尾分布的新机制

在研究教科书中出现的词频的情况下，科学家重新发明了导致西蒙发现的分布的随机机制。Simon分布由于产生了一种强化机制而被重尾，与现代的优先依恋概念相关。Simon发行版是最近推出的发行版的一个特例，它本身扩展了Sibuya发行版。我们展示了这种分布族的一些显着的统计特性，尤其是离散的自分解性。使用此问题并在环境中解决此问题后，研究了自然产生这种分布的其他随机过程，尤其是带有灾难的马尔可夫链模型。