【摘要】 本文研究了形如Cθ(u,v)=uv+θuavb(1—um)c(1—vn)d的一类新型广义FGM Copula的相关性.求解了其和谐性度量Kendall相关系数τ和Spearman相关系数ρ,论证了和谐性度量相比于线性相关系数的优越性.以泥石流地貌要素之沟床比降和流域高差为例,计算了这两个地貌要素的线性相关系数r、和谐型度量τ和ρ,说明两个和谐性度量τ和ρ之间的关系(3τ≈2ρ)适合用此新型广义FGM Copula描述.进一步对其中的6个参数a,b,c,d,m,n在各种不同取值下的τ和ρ的取值范围进行讨论,从而确定出一个具体的广义FGM Copula,它能够较好地拟合沟床比降和流域高差的相关结构.更多还原

【Abstract】 The correlation of a new class of general FGM Copulas: C θ (u, v) = uv + θu a v b (1 — u m ) c (1—v n ) d is studied in this paper. We resolve their concordance measures of the Kendall’s τ and Spearman’s ρ, and substantiate the advantage of the concordance measures as compared to the linear correlation coefficient. Taking the relief factors of debris flow of ditch bed gradient and drainage height difference as examples, we calculate the linear correlation coefficient r, the concordance measures of the Kendall’s τ and the Spearman’s ρ of the two relief factors. We further deduce the relationship between the Kendall’s τ and Spearman’s ρ to be 3τ ≈ 2ρ, which can be properly described by the proposed Copulas. Furthermore, the ranges of τ and ρ under different specifications of the six parameters of a, b, c, d, m, n are evaluated to set out a specific general FGM Copula. This copula can better fit the structure underlying the ditch bed gradient and the drainage height difference.更多还原