Asymptotics for the Hirsch Index

Abstract

Abstract. The last decade methods for quantifying the research output of individual researchers have become quite popular in academic policy making. The h-index (or Hirsch index) constitutes an interesting combined bibliometric volume/impact indicator that has attracted a lot of attention recently. It is now a common indicator, available for instance on the Web of Science. In this article, we establish the asymptotic normality of the empirical h-index. The rate of convergence is non-standard: , where f is the density of the citation distribution and n is the number of publications of a researcher. In case that the citations follow a Pareto-type respectively a Weibull-type distribution as defined in extreme value theory, our general result specializes well to results that are useful for practical purposes such as the construction of confidence intervals and pairwise comparisons for the h-index. A simulation study for the Pareto-type case shows that the asymptotic theory works well for moderate sample sizes already.