Two-step competition process leads to quasi power-law income distributions: Application to scientific publication and citation distributions

We apply a two-step competition process as a model to explain the distribution of citations (‘income’) over publications (‘work’). The first step is the competition amongst scientists to get their work published in better journals, and the second to get this work cited in these journals. Generally, citation distributions are supposed to follow a power law, like most other ‘income’ distributions. So far, no satisfactory theoretical model of citation distribution has been developed. On the basis of two Boltzmann type distribution functions of source publications, we derive a distribution function of citing publications over source publications. This distribution function corresponds very well to the empirical data. It is not a power law, but a modified Bessel-function. In our view, the model presented in this article has a more generic value, particularly in economics to explain observed income distributions.