A stochastic approach to the relation between the impact factor and the uncitedness factor

• We give a closed form relation between IF and UF involving a model parameter.
• The relation is time-dependent.
• A theoretical van Leeuwen–Moed lower bound is established.
• The form of the van Leeuwen–Moed diagram is explained.

Empirical analysis of the relationship between the impact factor – as measured by the average number of citations – and the proportion of uncited material in a collection dates back at least to van Leeuwen and Moed (2005) where graphical presentations revealed striking patterns. Recently Hsu and Huang (2012) have proposed a simple functional relationship. Here it is shown that the general features of these observed regularities are predicted by a well-established informetric model which enables us to derive a theoretical van Leeuwen–Moed lower bound. We also question some of the arguments of Hsu and Huang (2012) and Egghe (2013) while various issues raised by Egghe, 2008 and Egghe, 2013 are also addressed.