The h-index as an almost-exact function of some basic statistics

As is known, the h-index, h, is an exact function of the citation pattern. At the same time, and more generally, it is recognized that h is ‘‘loosely’’ related to the values of some basic statistics, such as the number of publications and the number of citations. In the present study we introduce a formula that expresses the h-index as an almost-exact function of some (four) basic statistics. On the basis of an empirical study—in which we consider citation data obtained from two different lists of journals from two quite different scientific fields—we provide evidence that our ready-to-use formula is able to predict the h-index very accurately (at least for practical purposes). For comparative reasons, alternative estimators of the h-index have been considered and their performance evaluated by drawing on the same dataset. We conclude that, in addition to its own interest, as an effective proxy representation of the h-index, the formula introduced may provide new insights into ‘‘factors’’ determining the value of the h-index, and how they interact with each other.