[R] Concordance and Kendall's tau in copula

[Martin Maechler]

>>>>> 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