Title: A statistical test for the Zipf's law by deviations from the Heaps' law,
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,
$\ldots$, and the probability of appearing the $i$'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.