A statistical test for the Zipf's law by deviations from the Heaps' law
Statistics Theory
2019-05-02 v3 Statistics Theory
Abstract
We explore a probabilistic model of an artistic text: words of the text are chosen independently of each other in accordance with a discrete probability distribution on an infinite dictionary. The words are enumerated 1, 2, , and the probability of appearing the 'th word is asymptotically a power function. Bahadur proved that in this case the number of different words depends on the length of the text is asymptotically a power function, too. On the other hand, in the applied statistics community, there exist statements supported by empirical observations, the Zipf's and the Heaps' laws. We highlight the links between Bahadur results and Zipf's/Heaps' laws, and introduce and analyse a corresponding statistical test.
Cite
@article{arxiv.1711.01083,
title = {A statistical test for the Zipf's law by deviations from the Heaps' law},
author = {Mikhail Chebunin and Artyom Kovalevskii},
journal= {arXiv preprint arXiv:1711.01083},
year = {2019}
}