English

Statistical analysis of the Hirsch Index

Statistics Theory 2014-07-29 v1 Digital Libraries Physics and Society Statistics Theory

Abstract

The Hirsch index (commonly referred to as h-index) is a bibliometric indicator which is widely recognized as effective for measuring the scientific production of a scholar since it summarizes size and impact of the research output. In a formal setting, the h-index is actually an empirical functional of the distribution of the citation counts received by the scholar. Under this approach, the asymptotic theory for the empirical h-index has been recently exploited when the citation counts follow a continuous distribution and, in particular, variance estimation has been considered for the Pareto-type and the Weibull-type distribution families. However, in bibliometric applications, citation counts display a distribution supported by the integers. Thus, we provide general properties for the empirical h-index under the small- and large-sample settings. In addition, we also introduce consistent nonparametric variance estimation, which allows for the implemention of large-sample set estimation for the theoretical h-index.

Keywords

Cite

@article{arxiv.1102.2701,
  title  = {Statistical analysis of the Hirsch Index},
  author = {Luca Pratelli and Alberto Baccini and Lucio Barabesi and Marzia Marcheselli},
  journal= {arXiv preprint arXiv:1102.2701},
  year   = {2014}
}
R2 v1 2026-06-21T17:25:44.017Z