Statistical regularities in the rank-citation profile of individual scientists

Citation counts and paper tallies are ubiquitous in the achievement ratings of individual scientists. As a result, there have been many recent studies which propose measures for scientific impact (e.g. the $h$-index) and the distribution of impact measures among scientists. However, being just a single number, the $h$-index cannot account for the full impact information contained in an author's set of publications. Alternative ``single-number'' indices are also frequently proposed, but they too suffer from the shortfalls of not being comprehensive. In this talk I will discuss an alternative approach, which is to analyze the fundamental properties of the {\it entire} rank-citation profile (from which all single-value indices are derived). Using the complete publication careers of $200$ highly-cited physicists and $100$ Assistant professors, I will demonstrate remarkable statistical regularity in the functional form of the rank-citation profile $c_{i}(r)$ for each physicist $i=1...300$. We find that $c_{i}(r)$ can be approximated by a discrete generalized beta distribution over the entire range of ranks $r$, which allows for the characterization and comparison of $c_{i}(r)$ using a common framework. Since two scientists can have equivalent $h_{i}$ values while having different $c_{i}(r)$, our results demonstrate the utility of a scaling parameter, $\beta_{i}$, in conjunction with $h_{i}$, to quantify a scientist's publication impact.