, Volume 17, Issue 3–4, pp 211–226 | Cite as

“Power law” version of Bradford's law: Statistical tests and methods of estimation

  • S. Naranan


Is is shown, using rigorous statistical tests, that the number of journals (J) carryingp papers in a given subject can be expressed as a simple power law functionJ(p)=K p −γ , K and γ being constants. The standard maximum likelihood method of estimating γ has been suitably modified to take acoount of the fact thatp is a discrete integer variable. The parameter γ entirely characterises the scatter of articles in journals in a given bibliography. According to a dynamic model proposed earlier by the author, γ is a measure of the relative growth rates of papers and journals pertaining to the subject.


Growth Rate Relative Growth Rate Likelihood Method Maximum Likelihood Method Integer Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    S. NARANAN, Bradford's law of science bibiography: An interpretation,Nature, 227 (Aug. 8 1970) 631.Google Scholar
  2. 2.
    S. NARANAN, Power law relations in science bibliography: A selfconsistent interpretation,Journal of Documentation, 27 (4) (1971) 83.Google Scholar
  3. 3.
    S. C. BRADFORD,Documentation, Crosby Lockwood, London, 1948.Google Scholar
  4. 4.
    B. C. VICKERY, Bradford's law of scattering,Journal of Documentation, 4 (1948) 198.Google Scholar
  5. 5.
    E. A. WILKINSON, The ambiguity of Bradford's law,Journal of Documentation, 28 (2) (1972) 122.Google Scholar
  6. 6.
    B. C. BROOKES, Bradford's law and the bibliography of science,Nature, 224 (Dec. 6, 1969) 953.Google Scholar
  7. 7.
    W. GOFFMAN, K. S. WARREN, Dispersion of papers among journals based on a mathematical analysis of two diverse medical literatures,Nature, 221 (March. 29, 1969) 1205.Google Scholar
  8. 8.
    W. GOFFMAN, T. G. MORRIS, Bradford's law and library acquisition,Nature, 226 (June. 6, 1970) 922.Google Scholar
  9. 9.
    R. KALLARD (Ed.)Holography, State of the Act Review, Optosonic Press New York, 1969.Google Scholar
  10. 10.
    G. K. ZIPF,The Psycho-Biology of Language, Houghton Mifflin Co., New York, 1935; M. I. T. Press, 1968 (paperback).Google Scholar
  11. 11.
    A. J. LOTKA, The frequency distribution of scientific productivity,Journal of the Washington Academy of Sciences 16 (1926) 317.Google Scholar
  12. 12.
    M. G. KENDALL, The bibliography of operational research,Operational Research Quartecly, II (1, 2) (1960) 31.Google Scholar
  13. 13.
    A. AVRAMESCU, Coherent informational energy and entropy,Journal of Documentation, 36 (Dec. 1980) 293.Google Scholar
  14. 14.
    N. KARMESHU, C. LIND, V. CANO, Rationales for Bradford's law,Scientometrics, 6 (1984) 233.Google Scholar
  15. 15.
    E. JAHNKE, F. EMDE,Tables of Functions with Formulae and Curves, 4th ed., Dover Publications, New York, 1945.Google Scholar
  16. 16.
    R. A. FISHER,Statistical Methods for Research Workers, 12th ed. Oliver and Boyd, London, 1954, pp. 78–113.Google Scholar
  17. 17.
    D. F. CRAWFORD, D. L. JAUNCEY, H. S. MURDOCH, Maximum-likelihood estimation of the slope from number-flux-density-counts of radio sources,Astrophysical Journal, 162 (Nov. 1970) 405.Google Scholar
  18. 18.
    M. G. KENDALL, A. STUART,The Advanced Theory of Statistics, Vol. 2, Charles Griffin & Co., London, 1961.Google Scholar

Copyright information

© Akadémiai Kiadó 1989

Authors and Affiliations

  • S. Naranan
    • 1
  1. 1.Tata Institute of Fundamental ResearchBombayIndia

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