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

Leo Egghe

Journal of the American Society for Information Science and Technology, 2007, vol. 58, issue 3, 452-454

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 nth citation distribution. We show that $$ h = ((1 - a^t )^{\alpha - 1} T)^{{1 \over \alpha }} $$ 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 $T^{{1 \over \alpha }}$.

Date: 2007
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