Abstract
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.
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References
I. Ajiferuke, Q. Burrell, J. Tague, Collaborative coefficient: A single measure of the degree of collaboration in research.Scientometrics 14 (1988) 421–433.
W. Glänzel, On Some Stopping Times of Citation Processes. From Theory to Indicators.Inf. Processing & Management, 28 (1) (1992) 53–60.
S.D. Haitun, Stationary Scientometric Distributions. Part I–III.Scientometrics 4 (1982) 5–25, 89–104, 181–194.
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.
J. Galambos, S. Kotz,Characterization of Probability Distributions, Springer New-York-Berlin Heidelberg, 1979.
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.
S. Kotz, D. N. Shanbhag, Some New Approaches to Probability Distributions.Adv. Appl. Probab. 12 (1980) 903–921.
W. Glänzel, Some Consequences of a Characterization Theorem Based on Truncated Moments,Statistics 21 4 (1990) 613–618.
W. Glänzel, A. Schubert, Pedictive Aspects of a Stochastic Model for Citation Processes.Proceedings of the 3. International Conference on Informetrics.
A. Schubert, W. Glänzel, Publication Dynamics. Models and Indicators.Scientometrics 20 (1991) 317–331.
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.
J.O. Irwin, The Generalized Waring Distribution; Parts I, II, III.J.R. Stat. Soc. A 138, 18–31, 204–227, 374–384 (1975).
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Glänzel, W., Schubert, A. A characterization of scientometric distributions based on harmonic means. Scientometrics 26, 81–96 (1993). https://doi.org/10.1007/BF02016794
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DOI: https://doi.org/10.1007/BF02016794