Generalized success-breeds-success principle leading to time-dependent informetric distributions

Abstract

The success-breeds-success principle (SBS principle) is reformulated in order to generate a general theory of source-item relationships. Several extensions are included such as a time-dependent probability α(t) for a new source to enter the system and general probabilities for new items to be produced by an old source. Moreover, we allow non steady-state situations. A new model for the expected probability E(P(t, n))—the expectation of the fraction of sources having n items at time t—is presented and compared with the SBS principle. As these models involve mathematically prohibited approximations, they are both compared with exact combinatorial calculations. Criteria for E(P(t, n)) to be decreasing (or not) in t as well as in n are given. It is observed that, even in the classical SBS framework, distributions which are not strictly decreasing in n are commonly encountered. Finally, introducing a quasi steady-state assumption, we show that nearly all classical frequency distributions, such as the beta function, the Lotka distribution, the truncated geometric distribution and the truncated Poisson distribution can be derived and explained via this generalized SBS principle. Note, however, that our models lead to time-dependent versions of these classical distributions. © 1995 John Wiley & Sons, Inc.