INDICES OF LITERATURE DISPERSION BASED ON QUALITATIVE ATTRIBUTES

The dispersion or ‘scatter’ of documents over some set of values of a document attribute is usually described by means of a frequency distribution. When the attribute is qualitative an order distribution can be defined, as in the usual descriptions of Bradford's law. A more succinct description is offered by an order statistic, such as Singleton's index. A novel order statistic, the ‘adapted Gini index’, is introduced and related to the conventional form of Bradford's law. Some simple properties of it are described. An alternative index of dispersion, not an order statistic, based on the relative entropy of the frequency distribution is also defined. For sets of bibliographies such indices themselves have distributions, and it is suggested that, in particular, the distribution pertaining to an indexed data base provides an objective characterization of the data base in so far as indexing terms have been applied to the items in it. A variety of experimental data is reported. This includes the distribution of two indices for samples of bibliographies taken from British Technology Index and Index Medicus, and studies of the variation of the indices with time when the attribute is that of journal title. Whether a new area of knowledge becomes less or more dispersed in its journals as it progresses depends in part on which index is chosen to represent the dispersion, and on whether a series of cumulative or cross‐section bibliographies is chosen.