, Volume 26, Issue 1, pp 81–96 | Cite as

A characterization of scientometric distributions based on harmonic means

  • W. Glänzel
  • A. Schubert
Invited Papers


The traditional stochastic approach to scientometric and bibliometric phenomena is based on measuring the absolute number of objects (e.g., publications, topics, citations). These measures reflect underlying rules such as the cumulative advantage principle and lead to classical statistical functions such as arithmetic mean and standard deviation. An alternative measure based on the contribution share of an individual object in the entirety of related objects reveals more about the coherence in the analyzed structure. This approach is connected with (conditional) harmonic means. The analysis of the properties of these statistical functions leads to a special urn-model distribution which has an analogous behaviour to that of the Waring distribution in connection with conditional arithmetic means. The new distribution combines specific properties (long tail, flexibility of the distribution shape) of the two scientometric favourites, the Waring and the negative binomial distribution. Five methods of parameter estimation are presented. The fit and the properties of this special urn-model distribution are illustrated by three scientometric examples, particularly, by two citation rate distributions with different shapes and one publication activity distribution with lacking zero frequencies.


Coherence Absolute Number Binomial Distribution Statistical Function Alternative Measure 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    I. Ajiferuke, Q. Burrell, J. Tague, Collaborative coefficient: A single measure of the degree of collaboration in research.Scientometrics 14 (1988) 421–433.CrossRefGoogle Scholar
  2. 2.
    W. Glänzel, On Some Stopping Times of Citation Processes. From Theory to Indicators.Inf. Processing & Management, 28 (1) (1992) 53–60.Google Scholar
  3. 3.
    S.D. Haitun, Stationary Scientometric Distributions. Part I–III.Scientometrics 4 (1982) 5–25, 89–104, 181–194.CrossRefGoogle Scholar
  4. 4.
    W. Glänzel, A. Schubert, The Cumulative Advantage Function. A Mathematical Formulation Based on Conditional Expectations and Its Application to Scientometric Distributions. In:L. Egghe, R. Rousseau (Eds);Informetrics 89/90, Elsevier Science Publishers B.V., 1990, 139–147.Google Scholar
  5. 5.
    J. Galambos, S. Kotz,Characterization of Probability Distributions, Springer New-York-Berlin Heidelberg, 1979.Google Scholar
  6. 6.
    W. Glänzel, A. Telcs, A. Schubert, Characterization by Truncated Moments and Its Application to Pearson-type Distributions,Z. Wahrscheinlichkeitstheorie u. verw. Gebiete, 66 (1984) 173–183.CrossRefGoogle Scholar
  7. 7.
    S. Kotz, D. N. Shanbhag, Some New Approaches to Probability Distributions.Adv. Appl. Probab. 12 (1980) 903–921.Google Scholar
  8. 8.
    W. Glänzel, Some Consequences of a Characterization Theorem Based on Truncated Moments,Statistics 21 4 (1990) 613–618.Google Scholar
  9. 9.
    W. Glänzel, A. Schubert, Pedictive Aspects of a Stochastic Model for Citation Processes.Proceedings of the 3. International Conference on Informetrics.Google Scholar
  10. 10.
    A. Schubert, W. Glänzel, Publication Dynamics. Models and Indicators.Scientometrics 20 (1991) 317–331.CrossRefGoogle Scholar
  11. 11.
    A. Telcs, W. Glänzel, A. Schubert, Characterization and Statistical Test Using Truncated Expectations for a Class of Skew Distributions.Mathematical Social Sciences, 10 (1985) 169–178.CrossRefGoogle Scholar
  12. 12.
    J.O. Irwin, The Generalized Waring Distribution; Parts I, II, III.J.R. Stat. Soc. A 138, 18–31, 204–227, 374–384 (1975).Google Scholar

Copyright information

© Akadémiai Kiadó 1993

Authors and Affiliations

  • W. Glänzel
    • 1
    • 2
  • A. Schubert
    • 2
  1. 1.Sozialwissenschaftliche Fakultät Fachgruppe PsychologieUniversität KonstanzKonstanz 1Germany
  2. 2.Library of the Hungarian Academy of SciencesInformation Science and Scientometrics Research Unit (ISSRU)BudapestHungary

Personalised recommendations