Log-log Convexity of Type-Token Growth in Zipf's Systems
物理与社会
2015-06-17 v1 数据分析、统计与概率
摘要
It is traditionally assumed that Zipf's law implies the power-law growth of the number of different elements with the total number of elements in a system - the so-called Heaps' law. We show that a careful definition of Zipf's law leads to the violation of Heaps' law in random systems, and obtain alternative growth curves. These curves fulfill universal data collapses that only depend on the value of the Zipf's exponent. We observe that real books behave very much in the same way as random systems, despite the presence of burstiness in word occurrence. We advance an explanation for this unexpected correspondence.
引用
@article{arxiv.1412.4577,
title = {Log-log Convexity of Type-Token Growth in Zipf's Systems},
author = {Francesc Font-Clos and Alvaro Corral},
journal= {arXiv preprint arXiv:1412.4577},
year = {2015}
}