BiCopTau2Par: Parameter of a bivariate copula for a given Kendall's tau...

In CDVine: Statistical Inference of C- And D-Vine Copulas

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 = rotated Clayton copula (180 degrees; “survival Clayton”) 14 = rotated Gumbel copula (180 degrees; “survival Gumbel”) 16 = rotated Joe copula (180 degrees; “survival Joe”) 23 = rotated Clayton copula (90 degrees) 24 = rotated Gumbel copula (90 degrees) 26 = rotated Joe copula (90 degrees) 33 = rotated Clayton copula (270 degrees) 34 = rotated Gumbel copula (270 degrees) 36 = rotated Joe copula (270 degrees) Note that two parameter bivariate copula families cannot be used.

Value

Parameter corresponding to the bivariate copula family and the value of Kendall's tau (τ).

No.	Parameter
1, 2	sin(τ π/2)
3, 13	max(0,2τ/(1-τ))
4, 14	max(1,1/(1-τ))
5	no closed form expression (numerical inversion)
6, 16	no closed form expression (numerical inversion)
23, 33	max(0,2τ/(1+τ))
24, 34	min(-1,-1/(1+τ))
26, 36	no closed form expression (numerical inversion)

Author(s)

Jakob Stoeber, Eike Brechmann

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.

See Also

BiCopTau2Par

Examples

## Example 1: Gaussian copula
tt1 = BiCopTau2Par(1,0.5)

# transform back
BiCopPar2Tau(1,tt1)


## Example 2: Clayton copula
BiCopTau2Par(3,0.4)

CDVine documentation built on May 2, 2019, 9:28 a.m.