Statistical Regularities in the Rank-Citation Profile of Scientists

Scientific Reports, Vol. 1, p. 181, 2011

29 Pages Posted: 21 Jul 2011 Last revised: 5 Dec 2011

Alexander Michael Petersen

University of California Merced, Ernest and Julio Gallo Management Program

H. Eugene Stanley

Boston University - Center for Polymer Studies

Sauro Succi

Istituto per le Applicazioni del Calcolo; University of Freiburg

Date Written: March 14, 2011

Abstract

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.

Keywords: scientific impact, rank distribution, citations, career achievement, Zipf Law

JEL Classification: D39, J24, J44

Suggested Citation

Petersen, Alexander Michael and Stanley, H. Eugene and Succi, Sauro, Statistical Regularities in the Rank-Citation Profile of Scientists (March 14, 2011). Scientific Reports, Vol. 1, p. 181, 2011 . Available at SSRN: https://ssrn.com/abstract=1889429

Alexander Michael Petersen (Contact Author)

University of California Merced, Ernest and Julio Gallo Management Program ( email )

School of Engineering
Science & Engineering 2, Suite 315
Merced, CA 95343
United States

H. Eugene Stanley

Boston University - Center for Polymer Studies ( email )

Boston, MA 02215
United States

Sauro Succi

Istituto per le Applicazioni del Calcolo ( email )

00161 Rome
Italy

University of Freiburg

Fahnenbergplatz
Freiburg, D-79085
Germany

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