Value Ranges of Spearman's Rho and Kendall's Tau of a Class of Copulas

We study a class of Copulas whose Kendall's τ and Spearman's ρ reach all the values in the intervals [0, 1/2] and [0, 3/4], and the relationship between them is 3τ = 2ρ. Taking the relief factors of drainage area and drainage height difference for example, some extreme data of the drainage area less than 0.35 being removed, this paper shows that the Spearman's ρ and Kendall's τ of the 935 set of remained data can be better prepared to that of our Copulas. In the last, two specific Copulas are given by calculating the parameters of the Copulas.