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We explore a probabilistic model of an artistic text: words of the text arechosen independently of each other in accordance with a discrete probabilitydistribution on an infinite dictionary. The words are enumerated 1, 2,$\ldots$, and the probability of appearing the $i$'th word is asymptotically apower function. Bahadur proved that in this case the number of different wordsdepends on the length of the text is asymptotically a power function, too. Onthe other hand, in the applied statistics community, there exist statementssupported by empirical observations, the Zipf's and the Heaps' laws. Wehighlight the links between Bahadur results and Zipf's/Heaps' laws, andintroduce and analyse a corresponding statistical test.

A statistical test for the Zipf's law by deviations from the Heaps' law