A stochastic independence approach for different measures of concentration and specialization

From data in the form of a two-way contingency table “Regions _ Sectors”, the concepts of specialization and concentration, built from the analysis of conditional distributions or profiles, is based on discrepancies among distributions: between profiles and a uniform distribution for absolute concepts; between profiles and the corresponding marginal distribution for the relative concepts; or between the joint distribution and the product of the marginal distributions for the global concept. This paper provides an extensive numerical analysis of measures derived from this approach and from other approaches used in the literature and shows that while the different measures under consideration display rather similar numerical behaviours, differences of ranking call for a particular care when interpreting the numerical results.