Zipf's law and the effect of ranking on probability distributions

International Journal of Theoretical Physics

Volumn 35, Issue 2, 1996, Pages 395-417

  Gunther R ^a   Levitin, L ^a,b   Schapiro, B ^a   Wagner, P ^a,c  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b Boston University   (United States)

^c UNIVERSITY OF COLOGNE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039337727     PISSN: 00207748     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02083823     Document Type: Article

References (23)

1. Auerbach, F. (1913). Das Gesetz der Bevölkerungskonzentration [The law of population concentration], Petermans Mitteilungen, 59, 74.
2. Borodovsky, M. Yu., and Gusein-Zade, S. M. (1989). A general rule for ranked series of codon frequencies in different genomes, Journal of Biomolecular Structure and Dynamics, 6, 1001.
3. Brokes, B. C. (1982). Qualitative analysis in the humanities: The advantage of ranking techniques, in Studies on Zipf's Law, H. Guiter and M. V. Arapov, eds., Studienverlag Dr. N. Brockmeyer, Bochum, Germany.
4. Frankhauser, P. (1991). The Pareto-Zipf-distribution of urban systems as stochastic process, in Models of Selforganization in Complex Systems, W. Ebeling, M. Peschel, and W. Weidlich, eds., Akademie Verlag, Berlin.
5. H. Guiter and M. V. Arapov, eds. (1982). Studies on Zipf's Law, Studienverlag Dr. N. Brockmeyer, Bochum, Germany.
6. Günther, R., and Wagner, P. (1995). Analysis of real texts, NRI Internal Report.
7. Günther, R., Schapiro, B., and Wagner, P. (1992). Physical complexity and Zipf's law, International Journal of Theoretical Physics, 31, 525-543.
8. Günther, R., Schapiro, B., and Wagner, P. (1993). Critical specific complexity: Recent results, NMI Internal Report.
9. Katsikas, A. A., and Nicolis, J. S. (1990). Chaotic dynamics of generating Markov partitions and linguistic sequences mimicking Zipf's law, Nuovo Cimento, 12D, 177.
10. Kohonen, T. (1982). Analysis of a simple self-organizing process, Biological Cybernetics, 44, 135-140.
11. Levitin, L. B., and Schapiro, B. (1993). Zipf's law and information complexity in an evolutionary system, in Proceedings IEEE International Symposium on Information Theory, San Antonio, Texas, p. 76.
12. Li, W. (1992). Random texts exhibit Zipf's-law-like word frequency distributions, IEEE Transactions on Information Theory, 38, 1842.
13. Mandelbrot, B. B. (1953). An information theory of the statistical structure of language, in Communication Theory, W. Jackson, ed., London, pp. 486-502.
14. Mandelbrot, B. B. (1983). The Fractal Geometry of Nature, Freeman, New York.
15. Nicolis, J. S., and Tsuda, I. (1989). On the parallel between Zipf's law and 1/f process in chaotic systems possessing coexisting attractors, Progress of Theoretical Physics, 82, 254-274.
16. Orlov, J. K. (1982). Ein Modell der Häufigkeitsstruktur des Vokabulars, in Studies on Zipf's Law, H. Guiter and M. V. Arapov, eds., Studienverlag Dr. N. Brockmeyer, Bochum, Germany.
17. Pareto, V. (1897). Cour d'Economie Politique, Lausanne and Paris [reprinted in Oevre Completes, Genf Droz].
18. Schapiro, B. (1994). An approach to the physics of complexity, Chaos, Solitons and Fractals, 4, 115-123.
19. Sharman, R. A. (1989). Observational evidence for a statistical model of language, IBM UKSC Report 205, September 1989.
20. Shreider, Yu. A. (1967). Theoretical derivation of text statistical features, Problemy Peredachi Informatsii, 3, 57-63.
21. Willis, J. C. (1922). Age and Area, Cambridge University Press, Cambridge.
22. Zipf, G. K. (1935). The Psychobiology of Language, Houghton-Miflin, Boston.
23. Zipf, G. K. (1949). Human Behavior and the Principle of Least Effort, Addison-Wesley, Cambridge, Massachusetts.