一类Copulas最优界的扰动及其相关性和对称性

Dependence measures and nonexchangeable degrees for perturbations of best-possible bounds of Copulas

对给定的奇异型Copula增加扰动项构造新的Copula.研究新Copula的和谐性度量Spearman′sρ,Kendall′sτ,Gini′sγ和Blomqvist′sβ与原Copula的比较.结果表明奇异型Copulas取Frechet-Hoeffding上下界M,W和单点值给定的Copulas最优上下界C U,C L时,增加扰动项后得到新的Copula可以拓宽相关性度量的范围.特别地,单点值给定的Copula的上下界C U,C L增加扰动项后构造新的Copula具有不可交换性,并度量了新Copula的不可交换性.

This paper constructed a new class of Copulas by putting the perturbation on given singular Copula.The dependence measures of new Copula,like Spearman′sρ,Kendall′sτ,Gini′sγand Blomqvist′sβwere compared to the original Copula.It turned out that the new Copula can broaden the range of correlation measures when the given singular Copula was Frechet-Hoeffding bounds M and W best-possible bounds for Copula specified at a single interior point C U,C L.Further,it found that the new Copula by putting perturbation on C U,C L were nonexchangeable,and measure the nonexchangeable degrees.