Lotka's Law

Description

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 x contributions in a given period is a fraction of the number making a single contribution, following the formula where a nearly always equals two, i.e., an approximate inverse-square law, where 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 discipline-specific.

Related formulas

Variables

Yrelative frequency of authors with X publications (dimensionless)
Cconstant depending on the specific field (dimensionless)
Xnumber of publications (dimensionless)
nconstant depending on the specific field (n~2) (dimensionless)