| The purpose of this thesis is to make a study of functions being used to measure concentration and diversity. As a means to differentiate among functions presented in literature the axiomatic method is used, the Lorenz curve playing a significant part as well.; First, the case is studied in which a number of items is distributed over a fixed number of sources. According to the distribution this leads to situations with different concentrations. By imposing more or less restricting requirements on functions a first classification of measures (type I, type II and type III) can be achieved for a fixed number of sources. The well-known Gini index e.g. is a concentration measure of type II, the coefficient of variation is a concentration measure of type III, and Shannon's index a diversity measure of type I. In this classification a measure of a particular type is automatically a measure of a type with a smaller number as well.; Next, the interesting problem is studied where situations with a different number of sources are compared as for concentration or diversity. A number of new measures is proposed, inferred from a shifted version of the Lorenz curve.; In the final chapter it is specified how to use these measures in informetrics: e.g. in the study of the evolution of bibliographies or in determining a set of core journals. |
