ExtremeValueCopulae {fCopulae}

Bivariate Extreme Value Copulae

Description

A collection and description of functions to investigate bivariate extreme value copulae.

Extreme Value Copulae Functions:

revCopula	Generates extreme value copula random variates,
pevCopula	computes extreme value copula probability,
devCopula	computes extreme value copula density,
revSlider	displays interactive plots of extreme value random variates,
pevSlider	displays interactive plots of extreme value probability,
devSlider	displays interactive plots of extreme value density.

Usage

revCopula(n, param = NULL, type = evList())
pevCopula(u = 0.5, v = u, param = NULL, type = evList(), 
    output = c("vector", "list"), alternative = FALSE )
devCopula(u = 0.5, v = u, param = NULL, type = evList(), 
    output = c("vector", "list"), alternative = FALSE )   

revSlider(B = 10)
pevSlider(type = c("persp", "contour"), B = 10)
devSlider(type = c("persp", "contour"), B = 10)

Arguments

alternative

[evRho][evTau][*evCopula] -
Should the probability be computed alternatively in a direct way from the probability formula or by default via the dependency function?

B

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

n

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

output

[*evCopula] -
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.

param

[*ev*][A*] -
distribution and copulae parameters. A numeric value or vector of named parameters as required by the copula specified by the variable type. If set to NULL, then the default parameters will be taken.

type

[*ev*][Afunc] -
the type of the extreme value copula. A character string selected from: "gumbel", "galambos", "husler.reiss", "tawn", or "bb5".
[evSlider] -
a character string specifying the plot type. Either a perspective plot which is the default or a contour plot with an underlying image plot will be created.

u, v

[*evCopula][*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.

Examples

## fCOPULA -
   getClass("fCOPULA")
   getSlots("fCOPULA")
   
## revCopula -
   # Not yet implemented
   # revCopula(n = 10, type = "galambos")
   
## pevCopula -
   pevCopula(u = grid2d(), type = "galambos", output = "list")
   
## devCopula -
   devCopula(u = grid2d(), type = "galambos", output = "list")
   
## AfuncSlider -
   # Generator, try:
   ## Not run: AfuncSlider()