论文标题
在两参数Yule-Simon分布上
On a two-parameter Yule-Simon distribution
论文作者
论文摘要
我们将经典的单参数Yule-Simon定律扩展到一个版本，具体取决于两个参数，部分出现在Bertoin [2019]中，在具有褪色内存的优先附件算法的上下文中。通过与年龄依赖性生殖率建立与一般分支过程的联系，我们研究了两参数Yule-Simon定律的尾巴反应行为，因为它已经在上述论文中启动了。最后，通过对分支过程的超级突变，我们提出了一个模型，该模型导致Yule-Simon定律的完整两参数范围，从而推广Simon [1955]在限制单词频率上的工作。
We extend the classical one-parameter Yule-Simon law to a version depending on two parameters, which in part appeared in Bertoin [2019] in the context of a preferential attachment algorithm with fading memory. By making the link to a general branching process with age-dependent reproduction rate, we study the tail-asymptotic behavior of the two-parameter Yule-Simon law, as it was already initiated in the mentioned paper. Finally, by superposing mutations to the branching process, we propose a model which leads to the full two-parameter range of the Yule-Simon law, generalizing thereby the work of Simon [1955] on limiting word frequencies.
