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The exact region determined by Blomqvist’s beta, Spearman’s footrule and Gini’s gamma

Cover: Journal of Computational and Applied Mathematics
  • SEB research

Authors:

Keywords:

Copula | Dependence concepts | Concordance measure | Gini’s gamma | Blomqvist’s beta | Spearman’s footrule

Abstract:

To quantify the degree of association between random variables, concordance measures are employed. To express such a degree, a single measure might give too much space, so several are used for comparison. In this paper we study the ternary relation between three well-known (weak) concordance measures, namely Blomqvist’s beta, Spearman’s footrule and Gini’s gamma. In other words, given the values of Blomqvist’s beta and Spearman’s footrule, we determine the degree of freedom a copula has at taking the value of Gini’s gamma. We explicitly determine the 3-dimensional region representing the relation. We also provide copulas where bounds of the region are attained.

The Sustainable Development Goals (SDGs) addressed in the article are:

  • SDG 4 – Quality education
  • SDG 9 – Industry, Innovation, Technology and Infrastructure

The article is published in:
Journal of computational and applied mathematics (ScienceDirect)

The content is freely accessible at:

The exact region determined by Blomqvist’s beta, Spearman’s footrule and Gini’s gamma

SDG's eng.