Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T05:24:01.211Z Has data issue: false hasContentIssue false
  • English
  • Français

On Zipf's law

Published online by Cambridge University Press:  14 July 2016

Michael Woodroofe  and
Bruce Hill
Michael Woodroofe
Affiliation:
University of Michigan
Bruce Hill
Affiliation:
University of Michigan
Get access Rights & Permissions [Opens in a new window]

Abstract

A Zipf's law is a probability distribution on the positive integers which decays algebraically. Such laws describe (approximately) a large class of phenomena. We formulate a model for such phenomena and, in terms of our model, give necessary and sufficient conditions for a Zipf's law to hold.

Keywords

CLASSICAL OCCUPANCY PROBLEMLAWS OF LARGE NUMBERS: WEAK CONVERGENCEREGULARLY VARYING FUNCTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 425 - 434
Copyright
Copyright © Applied Probability Trust 1975 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Feller, W. (1966) An Introduction to Probability Theory and its Applications , II. Wiley, New York.Google Scholar
Hill, B. (1970) Zipf's law and prior distributions for the composition of a population. J. Amer. Statist. Assoc. 65, 1220–1232.CrossRefGoogle Scholar
Hill, B. (1974) Rank frequency forms of Zipf's law. J. Amer. Statist. Assoc. 69, 1017–1026.CrossRefGoogle Scholar
Hill, B. and Woodroofe, M. (1975) Stronger forms of Zipf's law. J. Amer. Statist. Assoc. 70, 212–219.CrossRefGoogle Scholar
Simon, H. A. (1955) On a class of skew distribution functions. Biometrika 42, 425–440.CrossRefGoogle Scholar
Willis, J. C. (1922) Age and Area. Cambridge University Press.Google Scholar
Yule, G. U. (1924) A mathematical theory of evaluation based on the conclusions of Dr. J. C. Willis F.R.S. Phil. Trans. Roy. Soc. B 213, 21–87.Google Scholar
Zipf, G. K. (1949) Human Behavior and the Principle of Least Effort. Addison-Wesley, Reading, Mass.Google Scholar