Bivariate Archimedean Copulae

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Description

A collection and description of functions to investigate bivariate Archimedean copulae.

Archimedean Copulae Functions:

archmTau Computes Kendall's tau for Archimedean copulae,
archmRho computes Spearman's rho for Archimedean copulae,
archmTailCoeff computes tail dependence for Archimedean copulae,
archmTailPlot plots tail dependence for Archimedean copulae.

Usage

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archmTau(alpha = NULL, type = archmList(), lower = 1.0e-10)
archmRho(alpha = NULL, type = archmList(), method = c("integrate2d", "adapt"), 
    error = 1.0e-5)
    
archmTailCoeff(alpha = NULL, type = archmList())
archmTailPlot(alpha = NULL, type = archmList(), tail = c("Upper", "Lower"))

Arguments

alpha

the parameter of the Archemedean copula. A numerical value.

error

[archmRho] -
the error bound to be achieved by the integrate2d integration formula. A numeric value, by default error=1.0e-5.

lower

[archmTau] -
a numeric value setting the lower bound for the internal integration function integrate.

tail

[archmTailPlot] -
a character string, either "Upper" or "Lower" denoting which of the two tails should be displayed. By default the upper tail dependence will be considered.

type

the type of the Archimedean copula. A character string ranging beween "1" and "22". By default copula No. 1 will be chosen.

method

[archmRho] -
a character string that determines which integration method should be used, either "integrate2d" or "adapt". If the second method is selected the contributed R package "adapt" is required.

Value

The function pcopula returns a numeric matrix of probabilities computed at grid positions x|y.

The function parchmCopula returns a numeric matrix with values computed for the Archemedean copula.

The function darchmCopula returns a numeric matrix with values computed for thedensity of the Archemedean copula.

The functions Phi* return a numeric vector with the values computed from the Archemedean generator, its derivatives, or its inverse.

The functions cK and cKInv return a numeric vector with the values of the density and inverse for Archimedian copulae.

Author(s)

Diethelm Wuertz for the Rmetrics R-port.