Journal of the American Society for Information Science and Technology
Author cocitation analysis and Pearson's r
Journal of the American Society for Information Science and Technology - Special issue: Part II: Information seeking research
Letter to the editor: Pearson's r and author cocitation analysis: a commentary on the controversy
Journal of the American Society for Information Science and Technology
Rejoinder: in defense of formal methods
Journal of the American Society for Information Science and Technology
Information Processing and Management: an International Journal - Special issue: Formal methods for information retrieval
Construction of concentration measures for General Lorenz curves using Riemann-Stieltjes integrals
Mathematical and Computer Modelling: An International Journal
Hesitation degree-based similarity measures for intuitionistic fuzzy sets
International Journal of Information and Communication Technology
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This paper extends the Lorenz theory, developed in [L. Egghe, R. Rousseau, Symmetric and asymmetric theory of relative concentration and applications, Scientometrics 52 (2) (2001) 261-290], so that it can deal with comparing arrays of variable length. We show that in this case we need to divide the Lorenz curves by certain types of increasing functions of the array length N. We then prove that, in this theory, adding zeros to two arrays increases their similarity, a property that is not satisfied by the Pearson correlation coefficient. Among the many good similarity measures satisfying the developed Lorenz theory, we deduce the correlation coefficient of Spearman, hence showing that this measure can be used as a good measure of symmetric relative concentration (or similarity).