Time-dependent Lotkaian informetrics incorporating growth of sources and items

Authors:
L. Egghe
Affiliations:
Universiteit Hasselt (UHasselt), Campus Diepenbeek, Agoralaan, B-3590 Diepenbeek, Belgium and Universiteit Antwerpen (UA), Campus Drie Eiken, Universiteitsplein 1, B-2610 Wilrijk, Belgium
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

Citing 2
Cited 2

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

Journal of the American Society for Information Science and Technology
Item-time-dependent Lotkaian informetrics and applications to the calculation of the time-dependent h-index and g-index

Mathematical and Computer Modelling: An International Journal

Mathematical study of h-index sequences

Information Processing and Management: an International Journal
The Hirsch index and related impact measures

Annual Review of Information Science and Technology

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Abstract

In a previous article, static Lotkaian theory was extended by introducing a growth function for the items. In this article, a second general growth function-this time for the sources-is introduced. Hence this theory now comprises real growth situations, where items and sources grow, starting from zero, and at possibly different paces. The time-dependent size- and rank-frequency functions are determined and, based on this, we calculate the general, time-dependent, expressions for the h- and g-index. As in the previous article we can prove that both indices increase concavely with a horizontal asymptote, but the proof is more complicated: we need the result that the generalized geometric average of concavely increasing functions is concavely increasing.