Informetrics is the study of source-item relations in bibliographies; for example, authors may be sources and their publications may be items. This paper studies the stochastic process (called the information production process) leading to the determination of the expected number of sources with n items in a system with t items. The work extends previous studies by introducing new generalizations, such as a time-dependent probability that a new item entering the system will be produced by a source not previously in the system. The paper closes with a set of 29 references spanning the history of the subject, from its historical roots in economics and mathematical biology to work in the present decade, where the authors have been primary contributors.