The underlying process generating Lotka's Law and the statistics of exceedances

Abstract

Lotka's Law is a widely observed distribution of authors of scholarly papers and patents. Numerous studies over the past seventy years have found Lotka's Law describes production in fields as diverse as chemistry, economics, history, information science, musicology, patents and psychology. But previously the parameters for Lotka's Law were not linked to variables that could be measured or estimated during an individual's career. Here we show that the statistics of exceedances generates Lotka's Law. Specifically, the Frequency of production (papers or patents per year) and Lifetime (career duration) are exponentially distributed random variables. Empirical, phenomenological and mathematical development shows that, when suitably weighted, the product of Frequency and Lifetime produces Lotka's Law.