Functions of Concordance and Dependence with Related Measures

Abstract

Some functions that serve as building blocks for construction of a wider range of modes of concordance and dependence are pointed. We probe into interplays of such modes. From the standpoint of their conformity to stochastic dominance ordering of distributions within a Fréchet class, all such derived modes display some parallelism under certain conditions. We finally suggest a novel numeric measure of dependence that covers similar existing measures in literature.

Keywords:

• Circular ordering
• Concordance-dependence kernels
• Dependence indices
• Fréchet class
• Stochastic dominance

Mathematics Subject Classification:

• Primary 60E15, 62H20
• Secondary 60E99