Theory of first-citation distributions and applications
Mathematical and Computer Modelling: An International Journal
A proposal for a dynamic h-type index
Journal of the American Society for Information Science and Technology
Mathematical study of h-index sequences
Information Processing and Management: an International Journal
Developing a new collection-evaluation method: Mapping and the user-side h-index
Journal of the American Society for Information Science and Technology
Hirsch index rankings require scaling and higher moment
Journal of the American Society for Information Science and Technology
Scientometrics
Time-dependent Lotkaian informetrics incorporating growth of sources and items
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
The Hirsch index and related impact measures
Annual Review of Information Science and Technology
Identifying attractive research fields for new scientists
Scientometrics
Information Processing and Management: an International Journal
Hi-index | 0.00 |
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 $T^{{1 \over \alpha }}$. © 2007 Wiley Periodicals, Inc.