Statistical inference on the h-index with an application to top-scientist performance

Despite the huge amount of literature concerning the h-index, few papers have been devoted to its statistical analysis when a probabilistic distribution is assumed for citation counts. The present contribution mainly aims to divulge the inferential techniques recently introduced by Pratelli et al. (2012), by explaining the details for proper point and set estimation of the theoretical h-index. Moreover, some new achievements on simultaneous inference – addressed to produce suitable scholar comparisons – are carried out. Finally, the analysis of the citation dataset for the Nobel Laureates (in the last five years) and for the Fields medallists (from 2002 onward) is considered in order to exemplify the theoretical issues.

► A statistical model is assumed for the citation-count distribution.
► The statistical properties of the theoretical and empirical h-indexes are reviewed.
► The existing inferential techniques for point and set estimation of the theoretical h-index are illustrated.
► A new procedure to compare the h-index of different scholars is introduced.
► The considered methodologies are applied to the data of Nobel Laureates and Fields medallists.