Dynamic h-index: The Hirsch index in function of time

✍ Scribed by Leo Egghe

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 239 KB
• Volume: 58
• Category: Article
• ISSN: 1532-2882
• DOI: 10.1002/asi.20473

✦ Synopsis

Abstract

When there are a group of articles and the present time is fixed we can determine the unique number h being the number of articles that received h or more citations while the other articles received a number of citations which is not larger than h. In this article, the time dependence of the h‐index is determined. This is important to describe the expected career evolution of a scientist's work or of a journal's production in a fixed year. We use the earlier established cumulative n^th^ citation distribution. We show that

where a is the aging rate, α is the exponent of Lotka's law of the system, and T is the total number of articles in the group. For t = +∞ we refind the steady state (static) formula $h = T^{{1 \over \alpha }}$, which we proved in a previous article. Functional properties of the above formula are proven. Among several results we show (for α, a, T fixed) that h is a concavely increasing function of time, asymptotically bounded by $T^{{1 \over \alpha }}$.