BiCopTau2Par: Parameter of a bivariate copula for a given Kendall's tau value
Description
This function computes the parameter of a one parameter bivariate copula for a given value of Kendall's tau.
Usage
BiCopTau2Par(family, tau)
Arguments
tau
Kendall's tau value (numeric in [-1,1]).
family
An integer defining the bivariate copula family:
0 = independence copula
1 = Gaussian copula
3 = Clayton copula
4 = Gumbel copula
5 = Frank copula
6 = Joe copula
13<
Value
Parameter corresponding to the bivariate copula family and the value of Kendall's tau ($\tau$).
ll{
No. Parameter
1, 2 $\sin(\tau \frac{\pi}{2})$
3, 13 $\max(0,2\frac{\tau}{1-\tau})$
4, 14 $\max(1,\frac{1}{1-\tau})$
5 no closed form expression (numerical inversion)
6, 16 no closed form expression (numerical inversion)
23, 33 $\max(0,2\frac{\tau}{1+\tau})$
24, 34 $\min(-1,-\frac{1}{1+\tau})$
26, 36 no closed form expression (numerical inversion)
}
References
Joe, H. (1997).
Multivariate Models and Dependence Concepts.
Chapman and Hall, London.
Czado, C., U. Schepsmeier, and A. Min (2012).
Maximum likelihood estimation of mixed C-vines with application to exchange rates.
Statistical Modelling, 12(3), 229-255.