Reply to "Comment on 'A Scaling law beyond Zipf's law and its relation to Heaps' law'"

TL;DR

This paper defends a proposed scaling law for word-frequency distributions against criticisms, demonstrating its validity for frequencies above 10 and showing that the counter-example supports the original hypothesis.

Contribution

The authors clarify and reinforce the validity of their scaling law, countering previous claims of it being incorrect and providing evidence that supports their original approach.

Findings

Scaling law valid for absolute frequencies > 10

Counter-example supports the original scaling hypothesis

Criticisms of the law are unjustified

Abstract

In [arXiv:1404.1461], Yan and Minnhagen argue that the scaling law for the text-length dependence of word-frequency distributions proposed in [New J. Phys. 15 093033, arXiv:1303.0705] is "fundamentally incorrect" and "fundamentally impossible". In this note, we reason that such claims are clearly unjustified, with the scaling law being clearly valid for absolute frequencies greater than about 10. Further, we show that the very counter-example provided by Yan and Minnhagen [arXiv:1404.1461] fulfils our scaling hypothesis with excellent accuracy, at odds with Yan and Minnhagen's criticisms, and supporting our approach.