Asymptotics for the Hirsch Index

CentER Discussion Paper Series No. 2007-86

12 Pages Posted: 4 Nov 2007

See all articles by Jan Beirlant

Jan Beirlant

Catholic University of Leuven (KUL)

John H. J. Einmahl

Tilburg University - Department of Econometrics & Operations Research

Date Written: October 25, 2007


The last decade methods for quantifying the research output of individual researchers have become quite popular in academic policy making. The h- index (Hirsch, 2005) constitutes an interesting quality measure that has attracted a lot of attention recently. It is now a standard measure available for instance on the Web of Science. In this paper we establish the asymptotic normality of the empirical h-index. The rate of convergence is non-standard: ph=(1 nf(h)), where f is the density of the citation distribution and n the number of publications of a researcher. In case that the citations follow a Pareto-type or a Weibull-type distribution as defined in extreme value theory, our general result nicely specializes to results that are useful for constructing confidence intervals for the h-index.

Keywords: asymptotic normality; confidence interval; extreme value theory; research output; scientometrics; tail empirical process.

JEL Classification: C13, C14

Suggested Citation

Beirlant, Jan and Einmahl, John H. J., Asymptotics for the Hirsch Index (October 25, 2007). Available at SSRN: or

Jan Beirlant (Contact Author)

Catholic University of Leuven (KUL) ( email )

W. de Croylaan 54
Leuven, B-3001

John H. J. Einmahl

Tilburg University - Department of Econometrics & Operations Research ( email )

P.O. Box 90153
5000 LE Tilburg

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