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 = 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 ($\tau$).

No.

Parameter

1, 2

$sin(\tau \pi/2)$

3, 13

$max(0,2\tau/(1-\tau))$

4, 14

$max(1,1/(1-\tau))$

5

no closed form expression (numerical inversion)

6, 16

no closed form expression (numerical inversion)

23, 33

$max(0,2\tau/(1+\tau))$

24, 34

$min(-1,-1/(1+\tau))$

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.

Examples

Run this code

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

# transform back
BiCopPar2Tau(1,tt1)


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