Lotka's Law
Lotka's law is a law of scales established by Alfred J. Lotka in 1926 , which is used in scientometry .
General
Lotka's Law shows the relationship between the number of publications by a person and the number of people with an equally high publication output. It was established for the number of scientific journal articles and says that the number of people who write n articles is proportional to n −2 . Later results suggest an exponent of −1.7 instead of −2, which does not change the basic message of the law.
The general formulas are:
X = number of publications Y = relative frequency of authors with X publications n, C = constants (depending on the subject) [n ~ 2]
example
If 100 authors write an average of one article each in a certain period of time (see last line of the table), then the following table shows how many authors have written two, three etc. articles (for n = 2).
| items | Authors |
|---|---|
| 10 | 100/10 2 = 1 |
| 9 | 100/9 2 ≈ 1 (1.23 ..) |
| 8th | 100/8 2 ≈ 2 (1.56 ..) |
| 7th | 100/7 2 ≈ 2 (2.04 ..) |
| 6th | 100/6 2 ≈ 3 (2.77 ..) |
| 5 | 100/5 2 = 4 |
| 4th | 100/4 2 ≈ 6 (6.25) |
| 3 | 100/3 2 ≈ 11 (11.11 ..) |
| 2 | 100/2 2 = 25 |
| 1 | 100 |
In total, that's 294 articles written by 155 authors. Each author wrote 1.9 articles, rounded off on average.
Since its discovery, the law , which is among other things bibliometric , epistemological and sociological , has been repeatedly confirmed and established in other areas, e.g. B. in the number of employees and the extent of their contributions to open source projects. Lotka's law also applies to the authors and contributions of Wikipedia .
The number of citations per publication also decreases in the ratio n −2.5 to n −3 .
At the ends, the Lotka distribution is somewhat curved because the number of publications a person can publish is limited at the bottom (at least 1 article) and at the top (depending on the case).
William Bradford Shockley first pointed out in an article published in 1957 that different exponents are generated when considering multiple authorship of scientific papers and weighting the proportion of the individual authors. The weighting of the authorship means that e.g. For example, when working with four authors, 0.25 publications are assigned to each author.
A comparable but much simpler distribution is given by the Pareto distribution (80/20 rule), according to which 80% of the information requirement is covered by 20% of the sources.
literature
- Alfred J. Lotka: The frequency distribution of scientific productivity. In: Journal of the Washington Academy of Sciences. 16, 1926, pp. 317-323.
- Leo Egghe: Relations between the continuous and the discrete Lotka power function. In: Journal of the American Society for Information Science and Technology. 56, No. 7, 2005, pp. 664-668.
- Herbert A. Simon : Models of Man, Social and National. New York 1957, p. 160.
- Derek J. de Solla Price : Little Science, Big Science. Suhrkamp, Frankfurt 1974.
- Ronald Rousseau: Breakdown of the robustness property of Lotka Law - the case of adjusted counts for multiauthorship attribution. In: Journal of the American Society for Information Science. Vol. 43, Issue 10, December 1992, pp. 645-647.
Web links
- Brendan Rousseau & Ronald Rousseau: Cybermetrics. Issues Contents: Vol. 4 (2000): Paper 4. LOTKA: A program to fit a power law distribution to observed frequency data. at archive.is; Archived October 21, 2015.
Individual evidence
- ↑ Jakob Voss: Community writing processes in Wikipedia. Lecture at .hist 2006 (February 24, 2006). PDF file, 291 kB. ( Memento from September 27, 2007 in the Internet Archive )
- ^ William Shockley: On the statistics of individual variation of productivity in research laboratories. In: Proceedings of the IRE. 45, 3, 1957, pp. 279-290.