BiCopPar2Tau(family, par, par2=0)0 = independence copula
1 = Gaussian copula
2 = Student t copula (t-copula)
3 = Clayton copula
4 = Gumbel copula
5 = Frank par2 = 0).
Note that the degrees of freedom parameter of the t-copula does not need to be set,
because the theoretical Kendall's tau value of the t-copula is indep1, 2 $\frac{2}{\pi}\arcsin(\theta)$
3, 13 $\frac{\theta}{\theta+2}$
4, 14 $1-\frac{1}{\theta}$
5 $1-\frac{4}{\theta}+4\frac{D_1(\theta)}{\theta}$
with $D_1(\theta)=\int_0^\theta \frac{c/\theta}{\exp(x)-1}dx$ (Debey function)
6, 16 $\frac{2\theta-4+2\gamma +2\log2+\Psi(\frac{1}{\theta})+\Psi(\frac{2+\theta}{2\theta})}{\theta-2}$
with $\gamma=\lim_{n\to\infty}(\sum_{i=1}^n \frac{1}{i} -\log n)\approx 0.57$ (Euler's const.)
and $\Psi(x)=\frac{d}{dx}\log(\Gamma(x))$ (Digamma function)
7 $1-\frac{2}{\delta(\theta+2)}$
9 $1-\frac{2}{\delta(2-\theta)}+\frac{4}{\theta^2 \delta}B(\frac{2-\theta}{\theta},\delta+2)$
with $B(x,y)=\int_0^1 t^{x+1}(t-1)^{y-1}dt$ (Beta function)
23, 33 $\frac{\theta}{-\theta+2}$
24, 34 $-1-\frac{1}{\theta}$
26, 36 $\frac{2\theta+4-2*\gamma-2*\log2-\Psi(\frac{1}{-\theta})-\Psi(\frac{2-\theta}{-2\theta})}{\theta+2}$
}CDVinePar2Tau, BiCopTau2Par## Example 1: Gaussian copula
tt1 = BiCopPar2Tau(1,0.7)
# transform back
BiCopTau2Par(1,tt1)
## Example 2: Clayton copula
BiCopPar2Tau(3,1.3)Run the code above in your browser using DataLab