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On the Weak form of Zipf's law

Published online by Cambridge University Press:  14 July 2016

Wen-Chen Chen
Wen-Chen Chen*
Affiliation:
Carnegie–Mellon University
*
∗Postal address: Department of Statistics, Carnegie-Mellon University, Schenley Park, Pittsburgh, PA 15213, U.S.A.
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Abstract

Zipf's laws are probability distributions on the positive integers which decay algebraically. Such laws have been shown empirically to describe a large class of phenomena, including frequency of words usage, populations of cities, distributions of personal incomes, and distributions of biological genera and species, to mention only a few. In this paper we present a Dirichlet–multinomial urn model for describing the above phenomena from a stochastic point of view.

We derive the Zipf's law under certain regularity conditions; some limit theorems are also obtained for the urn model under consideration.

Keywords

ASYMPTOTIC NORMALITIESCONVERGENCE IN PROBABILITYCONVERGENCE IN DISTRIBUTIONDIRICHLET–MULTINOMIAL URN MODELMAXIMUM LIKELIHOOD ESTIMATEZIPF'S LAW
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 611 - 622
Copyright
Copyright © Applied Probability Trust 1980 

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