Bivariate Archimedean Copulae

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Description

A collection and description of functions concerned with the generator function for the Archimedean copula and with functions for setting and checking the distributional parameters.

Functions:

evList Returns list of implemented Archimedean copulae,
archmParam Sets default parameters for an Archimedean copula,
archmRange returns the range of valid rho values,
archmCheck checks if rho is in the valid range,
Phi Computes generator Phi, inverse and derivatives,
PhiSlider displays interactively generator function,
Kfunc computes copula density and its inverse,
KfuncSlider displays interactively density function.

Usage

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archmList()
archmParam(type = archmList())
archmRange(type = archmList(), B = Inf)
archmCheck(alpha, type = archmList())
      
Phi(x, alpha = NULL, type = archmList(), inv = FALSE, deriv = paste(0:2))
PhiSlider(B = 5)

Kfunc(x, alpha = NULL, type = archmList(), inv = FALSE, lower = 1.0e-8)
KfuncSlider(B = 5)

Arguments

alpha

[Phi*][*archmCopula] -
the parameter of the Archemedean copula. A numerical value.

B

[archmRange] -
the maximum slider menu value when the boundary value is infinite. By default this is set to B=Inf.
[*Slider] -
the maximum slider menu value when the boundary value is infinite. By default this is set to B=5.

deriv

[Phi] -
an integer value. Should the function itself, deriv="0", or the first deriv="1", or second deriv="2" derivative be evaluated?

inv

[Phi][Kfunc] -
a logical flag. Should the inverse function be computed?

lower

[Kfunc] -
a numeric value setting the lower bound for the internal root finding function uniroot.

type

[*archmCopula][Phi][Kfunc] -
the type of the Archimedean copula. A character string ranging beween "1" and "22". By default copula No. 1 will be chosen.

x

[Kfunc] -
a numeric value or vector ranging between zero and one.
[Phi] -
a numeric value or vector.

Value

The function Phi returns a numeric vector with the values computed from the Archemedean generator, its derivatives, or its inverse.

The function Kfunc returns a numeric vector with the values of the density and inverse for Archimedian copulae.

Author(s)

Diethelm Wuertz for the Rmetrics R-port.

References

RB Nelson - An Introduction to Copulas

Examples

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## archmList -
   # Return list of implemented copulae:
   archmList()