On a statistical h index

Abstract

The measurement of the quality of academic research is a rather controversial issue. Recently Hirsch has proposed a measure that has the advantage of summarizing in a single summary statistics the information that is contained in the citation counts of each scientist. From that seminal paper, a huge amount of research has been lavished, focusing on one hand on the development of correction factors to the h index and on the other hand, on the pros and cons of such measure proposing several possible alternatives. Although the h index has received a great deal of interest since its very beginning, only few papers have analyzed its statistical properties and implications. In the present work we propose a statistical approach to derive the distribution of the h index. To achieve this objective we work directly on the two basic components of the h index: the number of produced papers and the related citation counts vector, by introducing convolution models. Our proposal is applied to a database of homogeneous scientists made up of 131 full professors of statistics employed in Italian universities. The results show that while "sufficient" authors are reasonably well detected by a crude bibliometric approach, outstanding ones are underestimated, motivating the development of a statistical based h index. Our proposal offers such development and in particular confidence intervals to compare authors as well as quality control thresholds that can be used as target values. © 2013 Akadémiai Kiadó, Budapest, Hungary.