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A statistical test for the Zipf's law by deviations from the Heaps' law. / Chebunin, M. G.; Kovalevskii, A. P.

In: Сибирские электронные математические известия, Vol. 16, 01.01.2019, p. 1822-1832.

Research output: Contribution to journal › Article › peer-review

Harvard

Chebunin, MG & Kovalevskii, AP 2019, 'A statistical test for the Zipf's law by deviations from the Heaps' law', Сибирские электронные математические известия, vol. 16, pp. 1822-1832. https://doi.org/10.33048/semi.2019.16.129

APA

Chebunin, M. G., & Kovalevskii, A. P. (2019). A statistical test for the Zipf's law by deviations from the Heaps' law. Сибирские электронные математические известия, 16, 1822-1832. https://doi.org/10.33048/semi.2019.16.129

Vancouver

Chebunin MG, Kovalevskii AP. A statistical test for the Zipf's law by deviations from the Heaps' law. Сибирские электронные математические известия. 2019 Jan 1;16:1822-1832. doi: 10.33048/semi.2019.16.129

Author

Chebunin, M. G. ; Kovalevskii, A. P. / A statistical test for the Zipf's law by deviations from the Heaps' law. In: Сибирские электронные математические известия. 2019 ; Vol. 16. pp. 1822-1832.

BibTeX

@article{1fdc68f5a2e44837bca5a864db30f5c9,
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,:::, 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 as a function of the length of the text, again, asymptotically behaves like a power function. On the other hand, in the applied statistics community there are statements known as the Zipf's and Heaps' laws that are supported by empirical observations. We highlight the links between Bahadur results and Zipf's/Heaps' laws, and introduce and analyse a corresponding statistical test.",
keywords = "Heaps' law, Weak convergence, Zipf's law",
author = "Chebunin, {M. G.} and Kovalevskii, {A. P.}",
year = "2019",
month = jan,
day = "1",
doi = "10.33048/semi.2019.16.129",
language = "English",
volume = "16",
pages = "1822--1832",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - A statistical test for the Zipf's law by deviations from the Heaps' law

AU - Chebunin, M. G.

AU - Kovalevskii, A. P.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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 i'th word is asymptotically a power function. Bahadur proved that in this case the number of different words as a function of the length of the text, again, asymptotically behaves like a power function. On the other hand, in the applied statistics community there are statements known as the Zipf's and Heaps' laws that are supported by empirical observations. We highlight the links between Bahadur results and Zipf's/Heaps' laws, and introduce and analyse a corresponding statistical test.

AB - 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 i'th word is asymptotically a power function. Bahadur proved that in this case the number of different words as a function of the length of the text, again, asymptotically behaves like a power function. On the other hand, in the applied statistics community there are statements known as the Zipf's and Heaps' laws that are supported by empirical observations. We highlight the links between Bahadur results and Zipf's/Heaps' laws, and introduce and analyse a corresponding statistical test.

KW - Heaps' law

KW - Weak convergence

KW - Zipf's law

UR - http://www.scopus.com/inward/record.url?scp=85078653602&partnerID=8YFLogxK

U2 - 10.33048/semi.2019.16.129

DO - 10.33048/semi.2019.16.129

M3 - Article

AN - SCOPUS:85078653602

VL - 16

SP - 1822

EP - 1832

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 23258705