AssocMeasures {copula} | R Documentation |
These functions compute Kendall's Tau, Spearman's Rho, and the tail dependence index for bivariate copulas. Calibration is the inverse function: it calibrates the copula parameter given the value of Kendall's Tau or Spearman's Rho.
kendallsTau(copula, ...) spearmansRho(copula, ...) tailIndex(copula, ...) calibKendallsTau(copula, tau) calibSpearmansRho(copula, rho)
copula |
a "copula" object. |
tau |
a numerical value of Kendall's Tau in [-1, 1]. |
rho |
a numerical value of Spearman's Rho in [-1, 1]. |
... |
currently nothing. |
When there is no closed-form expression for Tau or Rho, numerical
integration from the adapt
package is used. For closed-form
expressions, see Frees and Valdez (1998).
The calibration function in fact returns a moment estimate of the parameter for single-parameter copulas.
E.W. Frees and E.A. Valdez (1998).Understanding relationships using copulas. North American Actuarial Journal, 2:1–25.
gumbel.cop <- gumbelCopula(3) kendallsTau(gumbel.cop) spearmansRho(gumbel.cop) tailIndex(gumbel.cop) ## let us compute the sample versions x <- rcopula(gumbel.cop, 200) cor(x, method = "kendall") cor(x, method = "spearman") ## compare with the true parameter value 3 calibKendallsTau(gumbel.cop, cor(x, method="kendall")[1,2]) calibSpearmansRho(gumbel.cop, cor(x, method="spearman")[1,2])