Duality revisited: Construction of fractional frequency distributions based on two dual Lotka laws

Fractional frequency distributions of e.g. authors with a certain (fractional) number of papers are very irregular and, therefore, not easy to model or to explain. This paper gives a first attempt to this by assuming two simple Lotka laws (with exponent 2) : one for the number of authors with n papers (total count here) and one for the number of papers with n authors, ncN. Based on an earlier made convolution model of Egghe, interpreted and reworked now for discrete scores, we are able to produce theoretical fractional frequency ' Permanent address. Research on this paper has been executed while this author was a visiting professor in LUC. He is grateful to LUC for financial support. distributions with only one parameter which are in very close agreement with the practical ones as found in a large dataset produced earlier by Rao. The paper hence also shows that (irregular) fractional frequency distributions are a consequence of Lotka's law and are not examples of breakdowns of this famous historical law.