Lotka's law,[1] named after Alfred J. Lotka, is one of a variety of special applications of Zipf's law. It describes the frequency of publication by authors in any given field. Let X be the number of publications, be the number of authors with publications, and be a constants depending on the specific field. Lotka's law states that .
In Lotka's original publication, he claimed . Subsequent research showed that varies depending on the discipline.
Equivalently, Lotka's law can be stated as , where is the number of authors with at least publications. Their equivalence can be proved by taking the derivative.
Assume that n=2 in a discipline, then as the number of articles published increases, authors producing that many publications become less frequent. There are 1/4 as many authors publishing two articles within a specified time period as there are single-publication authors, 1/9 as many publishing three articles, 1/16 as many publishing four articles, etc.
And if 100 authors wrote exactly one article each over a specific period in the discipline, then:
Portion of articles written | Number of authors writing that number of articles |
---|---|
10 | 100/102 = 1 |
9 | 100/92 ≈ 1 (1.23) |
8 | 100/82 ≈ 2 (1.56) |
7 | 100/72 ≈ 2 (2.04) |
6 | 100/62 ≈ 3 (2.77) |
5 | 100/52 = 4 |
4 | 100/42 ≈ 6 (6.25) |
3 | 100/32 ≈ 11 (11.111...) |
2 | 100/22 = 25 |
1 | 100 |
That would be a total of 294 articles and 155 writers, with an average of 1.9 articles for each writer.