Bivariate Archimedean Copulae

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Description

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

Archimedean Copulae Functions:

rarchmCopula Generates Archimedean copula variates,
parchmCopula computes Archimedean copula probability,
darchmCopula computes Archimedean copula density,
rarchmSlider displays interactive plots of variates,
parchmSlider displays interactive plots of probability,
darchmSlider displays interactive plots of density.

Special Copulae Functions:

rgumbelCopula Generates Gumbel copula variates,
pgumbelCopula computes Gumbel copula probability,
dgumbelCopula computes Gumbel copula density.

Usage

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rarchmCopula(n, alpha = NULL, type = archmList())
parchmCopula(u = 0.5, v = u, alpha = NULL, type = archmList(), output = 
    c("vector", "list"), alternative = FALSE )
darchmCopula(u = 0.5, v = u, alpha = NULL, type = archmList(), output = 
    c("vector", "list"), alternative = FALSE )
   
rarchmSlider(B = 10) 
parchmSlider(type = c("persp", "contour"), B = 10)
darchmSlider(type = c("persp", "contour"), B = 10)

rgumbelCopula(n, alpha = 2)
pgumbelCopula(u = 0.5, v = u, alpha = 2, output = c("vector", "list"))
dgumbelCopula(u = 0.5, v = u, alpha = 2, output = c("vector", "list"))

Arguments

alpha

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

alternative

[*Copula] -
Should the probability be computed alternatively ...

B

[*Slider] -
the maximum slider menu value when the boundary value is infinite. By default this is set to 10.

n

[rarchmCopula] -
the number of random deviates to be generated, an integer value.

output

[*archmCopula] -
output - a character string specifying how the output should be formatted. By default a vector of the same length as u and v. If specified as "list" then u and v are expected to span a two-dimensional grid as outputted by the function grid2d and the function returns a list with elements \$x, \$y, and \$z which can be directly used for example by 2D plotting functions.

type

[*archmCopula] -
the type of the Archimedean copula. A character string ranging beween "1" and "22". By default copula No. 1 will be chosen.
[*archmSlider] -
the type of the plot. A charcter string either specifying a perspective or contour plot.

u, v

[*archmCopula] -
two numeric values or vectors of the same length at which the copula will be computed. If u is a list then the the \$x and \$y elements will be used as u and v. If u is a two column matrix then the first column will be used as u and the the second as v.

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.