Predictive aspects of a stochastic model for citation processes

The model provides sufficiently good approximations for both the empirical mean value functions and the transition frequencies for the years 1985 and 1989 based on the number of citations the papers have received until 1982.

Abstract

A statistical model for citation processes is presented as a particular version of a nonhomogeneous birth process. The mean value function E(X(t) − X(s)|X(s) = i) and special transition probabilities such as P(X(t) − X(s) > 0|X(s) = 0) and P(X(t) − X(s) = 0|X(s) > 0) give essential information on the change of citation impact in time. It is shown that the mean value functions and transition probabilities can readily be calculated on the basis of known and estimated parameters. The analysis is illustrated by five examples. The citation rate for papers published in 1980 has been recorded in the period 1980 through 1989 in five science fields. The model provides sufficiently good approximations for both the empirical mean value functions and the transition frequencies for the years 1985 and 1989 based on the number of citations the papers have received until 1982.