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On the Weak form of Zipf's law

Published online by Cambridge University Press:  14 July 2016

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

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1980 

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