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.

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)

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