AssocMeasures {copula}R Documentation

Dependence measures for copulas

Description

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.

Usage

kendallsTau(copula, ...)
spearmansRho(copula, ...)
tailIndex(copula, ...)
calibKendallsTau(copula, tau)
calibSpearmansRho(copula, rho)

Arguments

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.

Details

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.

References

E.W. Frees and E.A. Valdez (1998).Understanding relationships using copulas. North American Actuarial Journal, 2:1–25.

Examples

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])

[Package copula version 0.7-6 Index]