# 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

 `1` ```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.

`BiCopTau2Par`

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```## 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 30, 2017, 12:18 a.m.