Asymptotics for the Hirsch Index

J. Beirlant, J.H.J. Einmahl

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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 theWeb 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.
Original languageEnglish
Place of PublicationTilburg
Number of pages12
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper


  • Asymptotic normality
  • confidence interval
  • extreme value theory
  • research output
  • scientometrics
  • tail empirical process.


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