Type/Token-Taken informetrics

Type/Token-Taken informetrics is a new part of informetrics that studies the use of items rather than the items itself. Here, items are the objects that are produced by the sources (e.g., journals producing articles, authors producing papers, etc.). In linguistics a source is also called a type (e.g., a word), and an item a token (e.g., the use of words in texts). In informetrics, types that occur often, for example, in a database will also be requested often, for example, in information retrieval. The relative use of these occurrences will be higher than their relative occurrences itself; hence, the name Type/Token-Taken informetrics. This article studies the frequency distribution of Type/Token-Taken informetrics, starting from the one of Type/Token informetrics (i.e., source-item relationships). We are also studying the average number mu(*) of item uses in Type/Token-Taken informetrics and compare this with the classical average number mu in Type/Token informetrics. We show that mu(*) greater than or equal to mu always, and that mu(*) is an increasing function of mu. A method is presented to actually calculate mu(*) from mu, and a given a, which is the exponent in Lotka's frequency distribution of Type/Token informetrics. We leave open the problem of developing non-Lotkaian Type/TokenTaken informetrics.