title: Duality revisited: construction of fractional frequency distributions based on two dual Lotka laws
abstract: Fractional frequency distributions of, for example, authors with a certain (fractional) number of papers are very irregular, and therefore not easy to model or to explain. The article gives a first attempt to this by as suming 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, n in N. Based on an earlier made convolution model of Egghe, interpreted and reworked now for discrete scores, we are able to produce theoretical fractional frequency 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 (1995). The article 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
keyphrases: dual Lotka laws convolution model discrete scores irregular fractional frequency distributions