# [R] Concordance and Kendall's tau in copula

Martin Maechler m@ech|er @end|ng |rom @t@t@m@th@ethz@ch
Tue Nov 7 10:03:58 CET 2023

>>>>> Steven Yen
>>>>>     on Tue, 7 Nov 2023 09:09:33 +0800 writes:

> Dear
> I estimate a sample selection model using the Clayton copula and Burr
> and Gaussian marginal. I need to derive ther Kendall'sw tau from the
> concordance coefficient by integration. I came across a way to do that
> in R long time ago but cannot find it again. Can somewone tell me what
> to read and what to use? Thank you.

> Steven Yen

I think you can estimate your model relatively easily using our
package {copula}  and the function  fitMvdc()

https://search.r-project.org/CRAN/refmans/copula/html/fitMvdc.html

MVDC := Multivariate Variate Distribution {built from} Copula

To solve the question you asked --- but would not need to answer if
using fitMvdc(),
you can use  e.g.,

> iTau(claytonCopula(), tau = 1.4)
[1] -7

or look up the formulas for tau() or its inverse 'iTau':

> copClayton using tau
function (theta)
{
theta/(theta + 2)
}

> copClayton using iTau
function (tau)
{
2 * tau/(1 - tau)
}

>

Best regards,
Martin

{and yes, consider getting our 'useR! Springer series book, as
it's the only "real" book, I've been a coauthor.. https://copula.r-forge.r-project.org/book/ }

--
Martin Maechler
ETH Zurich  and  R Core team

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