Lotka's law
Lotka's law, 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. Example 
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: 

That would be a total of 294 articles and 155 writers, with an average of 1.9 articles for each writer. Software 
 Friedman, A. 2015. "The Power of Lotka’s Law Through the Eyes of R" The Romanian Statistical Review. Published by National Institute of Statistics. - Software to fit a Lotka power law distribution to observed frequency data. See also
 Price's law

References

Further reading 
  — Chung and Cox analyze a bibliometric regularity in finance literature, relating Lotka's law to the maxim that "the rich get richer and the poor get poorer", and equating it to the maxim that "success breeds success". External links

The Journal of the Washington Academy of Sciences, vol. 16

Bibliometrics
Statistical laws