Stochastic modelling of the first-citation distribution

A simple stochastic model, based upon mixtures of non-homogeneous Poisson processes, is proposed to describe the citation process in the presence of ageing/obsolescence. Particular emphasis is placed upon investigation of the first-citation distribution where it is shown that in the presence of ageing there will inevitably be never-cited items. Conditions are given which show how the model is capable of modelling the various shapes of first-citation distributions reported in the literature. In particular, the essential link between the first-citation distribution and the obsolescence distribution is established.