Item-time-dependent Lotkaian informetrics and applications to the calculation of the time-dependent h- and g-index

Abstract

The model for the cumulative nth citation distribution, as developed in [L. Egghe, I.K. Ravichandra Rao, Theory of first-citation distributions and applications, Mathematical and Computer Modelling 34 (2001) 81–90] is extended to the general source–item situation. This yields a time-dependent Lotka function based on a given (static) Lotka function (considered to be valid for time t=∞). Based on this function, a time-dependent Lotkaian informetrics theory is then further developed by e.g. deriving the corresponding time-dependent rank–frequency function.

These tools are then used to calculate the dynamical (i.e. time-dependent) g-index (of Egghe) while also an earlier proved result on the time-dependent h-index (of Hirsch) is refound. It is proved that both indexes are concavely increasing to their steady state values for t=∞.