The estimation of the number of lost multi-copy documents: A new type of informetrics theory

Abstract

A probabilistic model is presented to estimate the number of lost multi-copy documents, based on retrieved ones. For this, we only need the number of retrieved documents of which we have one copy and the number of retrieved documents of which we have two copies. If we also have the number of retrieved documents of which we have three copies then we are also able to estimate the number of copies of the documents that ever existed (assumed that this number is fixed over all documents). Simulations prove the stability of the model. The model is applied to the estimation of the number of lost printed programmes of Jesuit theatre plays in the Provincia Flandro-Belgica before 1773. This Jesuit province was an administrative entity of the order, which was territorially slightly larger in extent than present day Flanders, the northern, Dutch-speaking part of Belgium. It is noted that the functional model P j for the fraction of retrieved documents with j copies is a size-frequency function satisfying ( P j+1 / P j )/( P j / P j−1 )<1 for all j. It is further noted that the “classical” size-frequency functions are different: Lotka's function satisfies the opposite inequality and the decreasing exponential one gives always 1 for the above ratio, hence showing that we are in a new type of informetrics theory. We also provide a mathematical rationale for the “book historical law” stating that the probability to lose a copy of a multi-copy document (i.e. an edition) is an increasing function of the size of the edition. The paper closes with some open problems and a description of other potential applications of this probabilistic model.