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. It states that the number of authors making n contributions is about $$1/n^{a}$$ of those making one contribution, where a nearly always equals two. More plainly, the number of authors publishing a certain number of articles is a fixed ratio to the number of authors publishing a single article. 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. Though the law itself covers many disciplines, the actual ratios involved (as a function of 'a') are very discipline-specific.

The general formula says:

X^n Y = C $$

or



Y = C / X^n $$,

where $$X$$ is the number of publications, $$Y$$ the relative frequency of authors with $$X$$ publications, and $$n$$ and $$C$$ are constants depending on the specific field ($$n \approx 2$$)

This law is believed to have applications in other fields for example in the military for fighter pilot kills.

Example
For 100 authors, who on average each write one article each over a specific period, we have also:

of those making one contribution, i.e. a power law, where a is often nearly 2. It is an empirical observation rather than a necessary result. This form of the law is as originally published and is sometimes referred to as the "discrete Lotka power function".