Double exponential model for first-citation processes

Abstract

The purpose of this article is to find a model for the first-citation or response distribution. Starting from plausible assumptions, we derive differential equations, whose solutions yield the requested functions. In fact, we propose two different double exponential distributions as candidates to describe the first-citation process. We found that some real data are best fitted by the first of these models and other by the second. We further note that Gompertz' curve plays an important role in this second model. These models can be used to predict the total number of articles in a fixed group that will ever be cited. We conclude that further research is needed to find out when one of the two models is more appropriate than the other.