On the Weak form of Zipf's law
- 1 September 1980
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 17 (3) , 611-622
- https://doi.org/10.2307/3212955
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
This publication has 9 references indexed in Scilit:
- Two Conditional Limit Theorems with ApplicationsThe Annals of Statistics, 1979
- Some Distributions Associated with Bose-Einstein StatisticsProceedings of the National Academy of Sciences, 1975
- On Zipf's lawJournal of Applied Probability, 1975
- Stronger Forms of Zipf's LawJournal of the American Statistical Association, 1975
- The Rank-Frequency Form of Zipf's LawJournal of the American Statistical Association, 1974
- Zipf's Law and Prior Distributions for the Composition of a PopulationJournal of the American Statistical Association, 1970
- On the compound negative multinomial distribution and correlations among inversely sampled pollen countsBiometrika, 1963
- ON A CLASS OF SKEW DISTRIBUTION FUNCTIONSBiometrika, 1955
- A Probability Distribution Derived from the Binomial Distribution by Regarding the Probability of Success as Variable between the Sets of TrialsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1948