Statistical Regularities in the Rank-Citation Profile of Scientists

Recent “science of science” research shows common regularities in the publication patterns of scientific papers across time and discipline. Here, we analyze the complete publication careers of 300 scientists and find remarkable regularity in the functional form of the rank-citation profile c_i(r) for each scientist i = 1...300. We find that the rank-ordered citation distribution c_i(r) can be approximated by a discrete generalized beta distribution (DGBD) over the entire range of ranks r, which allows for the characterization and comparison of c_i(r) using a common framework. The functional form of the DGBD has two scaling exponents, β_i and γ_i, which determine the scaling behavior of c_i(r) for both small and large rank r. The crossover between two scaling regimes suggests a complex reinforcement or positive-feedback relation between the impact of a scientist’s most famous papers and the impact of his/her other papers. Moreover, since two scientists with equivalent Hirsch h-index values may have different c_i(r) profiles, our results demonstrate the utility of the β_i parameter in conjunction with h, in order to quantify a scientist’s publication impact. We use the analytic properties of the DGBD to derive an exact expression for the crossover value r∗ which determines the set of distinguished papers for a given author