Skip to main content

Advertisement

Springer Nature Link
Log in

Stationary scientometric distributions

Part I. Different approximations

  • Published:
Scientometrics Aims and scope Submit manuscript

Abstract

Stationary distributions, i.e. distributions involving no time dependence, are analysed. The rank and frequency forms of statistical distributions are considered. On the basis of this consideration the approximations of stationary scientometric distributions are reviewed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

Notes and Refernces

  1. H. S. SICHEL, On a Distribution Law for Word Frequencies.J. of the Amer. Statistical Association 70 (1975) 352 part 1 542–547; J. H. HUBERT. Bibliometric Models for Journal Productivity,Social Indicators Research 4 (1977) 441–473; J. K. RAVICHANDRA RAO. The Distribution of Scientific Productivity and Social Change,J. of the Amer. Soc. for Inform. Science 31 (1980) 111–122.

    Google Scholar 

  2. J. VLACHY, Frequency Distribution of Scientific Performance. A Bibliography of Lotka's Law and Related Phenomena. —Scientometrics 1 (1978) 109–131.

    Google Scholar 

  3. J. B. ESTOUP.Gamma Stenographique (4th. ed.), Paris, 1916.

  4. G. K. ZIPF.Psycho-Biology of Language, Haughton Muffin, 1935.

  5. G. K. ZIPF,Human Behaviour and the Principle of Least Effort, adisson Wesley, Cambridge (Mass.), 1949.

    Google Scholar 

  6. G. SCARROTT, Will Zipf join Gauss? —New Scientist 62 (1974) 402–404.

    Google Scholar 

  7. J. C. WILLIS,Age and Area. Univ. Press, Cambridge, 1922.

    Google Scholar 

  8. A. J. LOTKA, The Frequency Distribution of Scientific Productivity,J. of Washington Academy of Sciences 16 (1926) 317–323.

    Google Scholar 

  9. S. C. BRADFORD. Sources of Information on Scientific Subjects, Engineering 26 (1934) January; S. C. BRADFORD.Documentation, Grosby Lookwood and Son LTD, London, 1948.

  10. R. A. FAIRTHORNE. Algebraic Representation of Storage and Retrieval Language.Proceeding of the International Conference on Scientific Information, National Academy of Sciences, Wash., DC., 1958.

  11. M. G. KENDALL, The Bibliography of Operational Research,Operational Research Quarterly 11 (1960) 31–36.

    Google Scholar 

  12. B. C. BROOKES, The Derivation and Application of the Bradford-Zipf Distribution. —J. of Documentation 24 (1968) 247–265.

    Google Scholar 

  13. P. F. COLE, A New Look at Reference Scattering,J. of Documentation 18 (1962) 58–64.

    Google Scholar 

  14. F. F. LAIMKUHLER. The Bradford Distribution,J. of Documentation 23 (1967) 197–207.

    Google Scholar 

  15. S. NARANAN. Power Law Relation in Science Bibliography: a Selfconsistent Interpretation,J. of Documentation 27 (1971) 83–97.

    Google Scholar 

  16. J. BOOKSTEIN. The Bibliometric Distributions,Library Quarterly 46 (1976) 416–423.

    Google Scholar 

  17. See: J. J. HUBERT,op cit., note 1. (1977) 441–473

    Google Scholar 

  18. B. MANDELBROT. Contribution a la theorie mathematique des jeux de communication. Ph. D. Thesis, Paris, Dec, 16, 1952, Publ. de l'Inst. de Statistique de l'Univ. de Paris, Vol. 2, No. 1. 2. p. 80–102, 1953.

  19. A. I. YABLONSKY, Stokhasticheskiye modeli nauchnoy deyatelnosti (Stochastic models of research activities). — In:Sistemniye issledovaniya. Yezhegodnik — 1975 (System Research Yearbook — 1975), Nauka, Moscow, 1976, p. 5–42; A. I. YABLONSKY. On fundamental Regularities of the Distribution of Scientific Productivity,Scientometrics 2 (1980) 3–34.

    Google Scholar 

  20. M. G. KENDALL, Natural Law in the Social Sciences,J. of the Royal Statistical Society 124 (1961) 4–16.

    Google Scholar 

  21. R. A. FAIRTHORNE. Empirical Hyperbolic Distribution (Bradford-Zipf-Mandelbrot) for Bibliometric Description and Prediction,J. of Documentation 25 (1969) 319–349.

    Google Scholar 

  22. A. I. YABLONSKY,op. cit., note 19..

    Google Scholar 

  23. D. J. de S. PRICE. Networks on Scientific Papers,Science 149 (1965) No. 3683, 520–525.

    Google Scholar 

  24. A. PLATZ. Psychology of the Scientist: Lotka's Law and Research Visibility,Psychological Reports 16 (1965) 566–568.

    Google Scholar 

  25. S. NARANAN.op. cit. note 15.

    Google Scholar 

  26. A. I. YABLONSKY.op. cit., note 19.

    Google Scholar 

  27. S. D. HAITUN. Chto takoye “tsitat-indeks” (What is the Citation Index”?Priroda (1980) No. 3, 40–51.

    Google Scholar 

  28. V. PARETO. Course d'economic politique, Paris, 1897.

  29. F. A. HAIGHT. Some Statistical Problems in Connection with Word Association Data.J. of Mathematical Psychology 3 (1966) 217–233.

    Google Scholar 

  30. L. S. KOZACHKOV, L. A. KHURSIN. Ob osnovnom veroyatnostnom raspredeleniyi naukovedeniya (On the Main Probability Distribution in Science of Science), In:Analiz zakonomernostey i prognpzirovaniye razvitiya nauki i tekhniki (Trend Analysis and Technological Forecasting), Vol. 1, Kiev, 1967, p. 42–45.

  31. M. K. BUCKLAND, A. HINDLE. Library Zipf (Letter),J. of Documentation 25 (1969) 154.

    Google Scholar 

  32. B. C. BROOKES. Bradford's Law and the Bibliography of Science,Nature 224 (1969) 953–956.

    Google Scholar 

  33. A. T. MITSEVICH. Issledovaniya structury nauchno-tekhnicheskoy informatsiyi po mashinostroyeniyu (Dissemination of Publications),Nauchno-tekhnicheskaya Informatsiya, Ser. 2 (1975) No. 5, p. 5–16.

    Google Scholar 

  34. C. H. BOSANQUET, Distribution of Word Frequencies. —Nature 179 (1957) 596.

    Google Scholar 

  35. D. J. de S. PRICE,Little Science, Big Science, Columbia Univ. Press, New-York-London, 1963.

    Google Scholar 

  36. H. T. DAVIS,The Analysis of Economic Time Series, The Principla Press Inc. Bloomington, Indiana, 1941, XIV.

    Google Scholar 

  37. G. U. YULE, A Mathematical Theory of Evolution Based on Conclusions of J. C. WILLIS,Phylosophical Transaction of the Royal Society Ser. B, 213 (1924) 21–87.

    Google Scholar 

  38. H. A. SIMON. On a Class of Skew Distribution Function,Biometrica 42 (1955) 425–440.

    Google Scholar 

  39. J. D. de S. PRICE, A General Theory of Bibliometric and Other Cumulative Advantage Processes,J. of the Amer. Soc. for Inform. Science 27 (1967) 292–306.

    Google Scholar 

  40. M. G. KENDALL.op. cit., note 11..

    Google Scholar 

  41. J. O. IRWIN. The Generalized Wording Dsitribution Applied to Accident Theory,J. of the Royal Statistical Society Ser. A, 131 (1968) Part 2, 205–225; 138 (1975) Part 2, 204–227; 138 (1975) Part 3, 373–384.

    Google Scholar 

  42. C. J. CROWLEY. The Distribution of Citations to Scientific Parameters: a Model. Chicago, April 1975 (unpublished). See: J. D. de S. PRICE. op. cit., note 39.A General Theory of Bibliometric and Other Cumulative Advantage Processes,J. of the Amer. Soc. for Inform. Science 27 (1967) 292–306.

  43. J. K. RAVICHANDRA RAO.op. cit., note 1..

    Google Scholar 

  44. E. B. WILLIAMS. The Number of Publications Written by Biologists,Annaly of Eugenics 12 (1944) 143–144.

    Google Scholar 

  45. E. B. WILLIAMS.op. cit., note 44. (1944) 143–144.

    Google Scholar 

  46. I. J. GOOD. The Population Frequencies of Species and the Estimation of Population Parameters,Biometrics 40 (1953) 237–264.

    Google Scholar 

  47. I. J. GOOD.op. cit., note 46..

    Google Scholar 

  48. W. SHOKLEY. On the Statistics of Individual Variation of Productivity in Research Laboratories,Proceedings of IRE 45 (1957) 279–290.

    Google Scholar 

  49. D. PELZ, F. ANDREWS.Scientists in Organization, Productive Climates for Research and Development, Willey, New-York e.a., 1960; 2nd ed., Michigan, 1976.

    Google Scholar 

  50. D. J. de S. PRICE, D. de BEAVER. Collaboration in an Invisible CollegesAmer. Psychologist 21 (1966) No. 11.

    Google Scholar 

  51. R. F. VASILYEV. O kolichestve publikatsiy i chastote ikh tsitirovaniya kak naukometricheskikh pokazatelyakh (Publication Quantity and Frequency of Citation as Science Indicators). — In: Materialy k simpoziumuIssledovaniye operatsiy i analiz razvitiya nauki (Proc. of Symp. on Operation Research and Science Development), Moscow, 1976, p. 60–70.

  52. A. A. IGNATYEV, A. I. YABLONSKY. Analiticheskiye struktury nauchnoy kommunikatsiyi (Analytic Structures of Science Communication), In: Sistemniye issledovaniya, Yezhegodnik, 1975 (System Research Yearbook-1975), Moscow, 1976, p. 64–81.

  53. L. MANTELL. On Laws of Special Abilities and the Production of Scientific Literature,Amer. Documentation 17 (1966) 8–16.

    Google Scholar 

  54. M. G. BULMER. On Fitting the Poisson lognormal Distribution to Species-Abundance Data,Biometrics 30 (1974) 101–110.

    Google Scholar 

  55. H. S. SICHEL.op cit., note 1.

    Google Scholar 

  56. G. U. YULE.A Statistical Study of Vocabulary. Cambridge, England, Univ. Press, 1944.

    Google Scholar 

  57. G. HERDAN.Language as Choice and Chance. Groningen, Noordhoff, 1956.

    Google Scholar 

  58. See: H. S. SICHEL,op. cit. note 1.

    Google Scholar 

  59. See, for example: M. G. BULMER,op. cit., note 54. H. S. SICHEL, op. cit, note 1;On a Distribution Law for Word Frequencies.J. of the Amer. Statistical Association 70 (1975) 352; R. C. COILE. Lotka's Frequency Distribution of Scientific Productivity,J. of the Amér. Soc. for Inform. Science 28 (1977) 366–370; P. PRAUNLICH, M KROLL. Bradford's Distribution: a New Formulation,J. of the Amer. Soc. for Inform. Science 29 (1978) 51–55; T. RADHAKRISHNAN, R. KERNIZAN. Lotka's Law and Computer Science Literature,J. of the Amer. Soc. for Inform. Science 30 (1979) 51–64; J. K. RAVICHANDRA RAO, op. cit., note 1. The Distribution of Scientific Productivity and Social Change,J. of the Amer. soc. for Inform. Science 31 (1980) 111–122.

    Google Scholar 

  60. See: M. V. ARAPOVA, Ye. V. EFIMOVA, Yu. A. SHREIDER. O smysle rangovykh raspredeleniy (On Sense of Rank Distributions),Nauchno-tekhnicheskaya Informatsiya Ser 2 (1975) No. 1, 9–20; A. BOOKSTEIN, op. cit., note 16; The Bibliometric Distributions,Library Quarterly 46 (1976) 416–423; B. C. BROOKES, J. M. GRIFFITS. Frequency-rank Distributions,J. of the Amer. Soc. for Inform. Science 29 (1978) 5–13; J. J. HUBERT. A Relationship between Two Forms of Bradford's Law, J. of the Amer. Soc. for Inform. Science 29 (1978) 159–161; A. I. YABLONSKY, 1980, op. cit., note 19. On fundamental Regularities of the Distribution of Scientific Productivity,Scientometrics 2 (1980) 3–34.

    Google Scholar 

  61. Yablonsky [see: A. I. YABLONSKY, 1980, op. cit., note 19] On fundamental Regularities of the Distribution of Scientific Productivity,Scientometrics 2 (1980) 3–34 derived the expressions (B. 7) and (B. 8) (last at γ=1) at O ≤ r ≤ N (see definition (A. 2) in Appendix A). The author obtained these expressions independently.

  62. See: A. I. YABLONSKY, 1980, op. cit., note 19. On fundamental Regularities of the Distribution of Scientific Productivity,Scientometrics 2 (1980) 3–34. The author noticed this phenomenon regardless.

Download references

Author information

Authors and Affiliations

  1. Institute of the History of Science and Technology, Academy of Sciences of the USSR, Staropansky per. 1/5, Moscow, (USSR)

    S. D. Haitun

Authors
  1. S. D. Haitun
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Haitun, S.D. Stationary scientometric distributions. Scientometrics 4, 5–25 (1982). https://doi.org/10.1007/BF02098003

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02098003

Keywords