A remarkable example in three-dimensional informetrics. The geometric law: Distribution of use or distribution of structure?

This article offers a mathematical model that is in line with three-dimensional informetrics. We show that the geometric distribution - often found in informetric processes of use to model the distributions of book loans in libraries, of citations, or of journals downloads in scientific databases - plays a surprising role. To show this, we infer the existence of another distribution, which we have called “distribution of structure”. Distributions of use and distributions of structure are the two key processes in our three-dimensional IPP (Information Production Process). Furthermore, we indirectly introduce the time dependence of these distributions through the concept of information obsolescence. To demonstrate the theorems, we use the properties of probability-generating functions (PGF).