A Heuristic Study of the First-Citation Distribution

Abstract

The first-citation distribution, i.e. the cumulative distribution of the time period between publication of an article and the time it receives its first citation, has never been modelled by using well-known informetric distributions. An attempt to this is given in this paper. For the diachronous aging distribution we use a simple decreasing exponential model. For the distribution of the total number of received citations we use a classical Lotka function. The combination of these two tools yield new first-citation distributions.

The model is then tested by applying nonlinear regression techniques. The obtained fits are very good and comparable with older experimental results of Rousseau and of Gupta and Rousseau. However our single model is capable of fitting all first-citation graphs, concave as well as S-shaped; in the older results one needed two different models for it.

Our model is the function

$$\Phi {\text{(t}}_{\text{1}} {\text{) = }}\gamma (1 - a^{{\text{t}}_{\text{1}} } )^{\alpha - 1} {\text{ }}.$$

Here γ is the fraction of the papers that eventually get cited, t₁ is the time of the first citation, a is the aging rate and α is Lotka's exponent. The combination of a and α in one formula is, to the best of our knowledge, new. The model hence provides estimates for these two important parameters.