2008/08/22 by M. D. Taylor, Taylor, M. D.
Mathematics · #60E05 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #msc:60E05 #stat.TH
paper · pdf · doi:10.48550/arxiv.0808.3105
arxiv created 2008/08/22 · arxiv updated 2009/12/01
We explore the consequences of a set of axioms which extend Scarsini's axioms for bivariate measures of concordance to the multivariate case and exhibit the following results: (1) A method of extending measures of concordance from the bivariate case to arbitrarily high dimensions. (2) A formula expressing the measure of concordance of the random vectors (± X1,...,± Xn) in terms of the measures of concordance of the "marginal" random vectors (Xi1,...,Xik). (3) A method of expressing the measure of concordance of an odd-dimensional copula in terms of the measures of concordance of its even-dimensional marginals. (4) A family of relations which exist between the measures of concordance of the marginals of a given copula.