Statistical regularities in the rank-citation profile of scientists

Recent science of science research shows that scientific impact measures for journals and individual articles have quantifiable regularities across both time and discipline. However, little is known about the scientific impact distribution at the scale of an individual scientist. We analyze the aggregate production and impact using the rank-citation profile c_i(r) of 200 distinguished professors and 100 assistant professors. For the entire range of paper rank r, we fit each c_i(r) to a common distribution function. Since two scientists with equivalent Hirsch h-index can have significantly different c_i(r) profiles, our results demonstrate the utility of the bi scaling parameter in conjunction with hi for quantifying individual publication impact. We show that the total number of citations C tallied from a scientist’s N_i papers scales as C_i ~ h_i^\beta_i . Such statistical regularities in the input-output patterns of scientists can be used as benchmarks for theoretical models of career progress