# assocMeasures

0th

Percentile

##### Dependence Measures for Bivariate Copulas

These functions compute Kendall's tau, Spearman's rho, and the tail dependence index for bivariate copulas. iTau and iRho, sometimes called “calibration” functions are the inverses: they determine (“calibrate”) the copula parameter (which must be one-dimensional!) given the value of Kendall's tau or Spearman's rho.

Keywords
multivariate
##### Usage
tau (copula, …)
rho (copula, …)
lambda(copula, …)
iTau (copula, tau, …)
iRho (copula, rho, …)
##### Arguments
copula

an R object of class "'>copula" (or also "'>acopula" or "'>nacopula"; note however that some methods may not be available for some copula families).

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

The calibration functions iTau() and iRho() in fact return a moment estimate of the parameter for one-parameter copulas.

When there are no closed-form expressions for Kendall's tau or Spearman's rho, the calibration functions use numerical approximation techniques (see the last reference). For closed-form expressions, see Frees and Valdez (1998). For the t copula, the calibration function based on Spearman's rho uses the corresponding expression for the normal copula as an approximation.

##### References

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

Iwan Kojadinovic and Jun Yan (2010) Comparison of three semiparametric methods for estimating dependence parameters in copula models. Insurance: Mathematics and Economics 47, 52--63.

The '>acopula class objects have slots, tau, lambdaL, and lambdaU providing functions for tau(), and the two tail indices lambda(), and slot iTau for iTau(), see the examples and copGumbel, etc.

##### Aliases
• tau
• rho
• kendallsTau
• spearmansRho
• iTau
• iRho
• calibKendallsTau
• calibSpearmansRho
• tailIndex
• lambda
• tau-methods
• tau,ANY-method
• tau,copula-method
• tau,archmCopula-method
• tau,amhCopula-method
• tau,claytonCopula-method
• tau,frankCopula-method
• tau,gumbelCopula-method
• tau,indepCopula-method
• tau,lowfhCopula-method
• tau,upfhCopula-method
• tau,joeCopula-method
• tau,normalCopula-method
• tau,tCopula-method
• tau,fgmCopula-method
• tau,plackettCopula-method
• tau,moCopula-method
• tau,galambosCopula-method
• tau,huslerReissCopula-method
• tau,tawnCopula-method
• tau,tevCopula-method
• tau,evCopula-method
• tau,acopula-method
• tau,nacopula-method
• tau,rotCopula-method
• rho-methods
• rho,ANY-method
• rho,copula-method
• rho,normalCopula-method
• rho,tCopula-method
• rho,claytonCopula-method
• rho,frankCopula-method
• rho,gumbelCopula-method
• rho,amhCopula-method
• rho,fgmCopula-method
• rho,plackettCopula-method
• rho,moCopula-method
• rho,galambosCopula-method
• rho,huslerReissCopula-method
• rho,indepCopula-method
• rho,lowfhCopula-method
• rho,upfhCopula-method
• rho,tawnCopula-method
• rho,tevCopula-method
• rho,evCopula-method
• rho,acopula-method
• rho,nacopula-method
• rho,rotCopula-method
• lambda-methods
• lambda,ANY-method
• lambda,copula-method
• lambda,evCopula-method
• lambda,claytonCopula-method
• lambda,frankCopula-method
• lambda,gumbelCopula-method
• lambda,indepCopula-method
• lambda,lowfhCopula-method
• lambda,upfhCopula-method
• lambda,amhCopula-method
• lambda,joeCopula-method
• lambda,plackettCopula-method
• lambda,moCopula-method
• lambda,normalCopula-method
• lambda,tCopula-method
• lambda,acopula-method
• lambda,nacopula-method
• lambda,rotCopula-method
• iTau-methods
• iTau,ANY-method
• iTau,copula-method
• iTau,ellipCopula-method
• iTau,normalCopula-method
• iTau,tCopula-method
• iTau,archmCopula-method
• iTau,amhCopula-method
• iTau,claytonCopula-method
• iTau,frankCopula-method
• iTau,gumbelCopula-method
• iTau,joeCopula-method
• iTau,plackettCopula-method
• iTau,fgmCopula-method
• iTau,galambosCopula-method
• iTau,huslerReissCopula-method
• iTau,tawnCopula-method
• iTau,tevCopula-method
• iTau,nacopula-method
• iTau,acopula-method
• iTau,rotCopula-method
• iRho-methods
• iRho,ANY-method
• iRho,copula-method
• iRho,ellipCopula-method
• iRho,normalCopula-method
• iRho,tCopula-method
• iRho,archmCopula-method
• iRho,claytonCopula-method
• iRho,frankCopula-method
• iRho,gumbelCopula-method
• iRho,galambosCopula-method
• iRho,huslerReissCopula-method
• iRho,tawnCopula-method
• iRho,tevCopula-method
• iRho,plackettCopula-method
• iRho,fgmCopula-method
• iRho,nacopula-method
• iRho,rotCopula-method
##### Examples
# NOT RUN {
gumbel.cop <- gumbelCopula(3)
tau(gumbel.cop)
rho(gumbel.cop)
lambda(gumbel.cop)
iTau(joeCopula(), 0.5)
# }
# NOT RUN {
<!-- %%--- more "tests" are in ../tests/moments.R -->
# }
# NOT RUN {
stopifnot(all.equal(tau(gumbel.cop), copGumbel@tau(3)),

all.equal(lambda(gumbel.cop),
c(copGumbel@lambdaL(3), copGumbel@lambdaU(3)),
check.attributes=FALSE),

all.equal(iTau (gumbel.cop, 0.681),
copGumbel@iTau(0.681))
)

## let us compute the sample versions
x <- rCopula(200, gumbel.cop)
cor(x, method = "kendall")
cor(x, method = "spearman")
## compare with the true parameter value 3
iTau(gumbel.cop, cor(x, method="kendall" )[1,2])
iRho(gumbel.cop, cor(x, method="spearman")[1,2])
# }

Documentation reproduced from package copula, version 0.999-19, License:

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