World Flash on Basic Research

Summary

An incomplete bibliography (or, more generally, an incomplete Information Production Process (IPP)) can be considered as a sample from a complete one. Sampling can be done in the sources or in the items. The simplest sampling technique is the systematic one where every k<Superscript>th</Superscript> source or k<Superscript>th</Superscript> item is taken (alternatively: deleted) (k&Icirc;&ucirc;). In this paper we give a definition of systematic sampling in items and sources in the framework of an IPP in which we have continuous variables. We prove the theorem that in such IPPs we have a Lotkaian size-frequency function (i.e. a decreasing power function) if and only if systematic sampling in sources is the same as systematic sampling in items. In this proof we use the well-known characterization of power functions as scale-free functions.