aaaCopulaClass: Bivariate Copula Class

In fCopulae: Rmetrics - Bivariate Dependence Structures with Copulae

Bivariate Copula Class

Description

A collection and description of functions to specify the copula class and to investigate bivariate Frechet copulae.

The class representation and methods are:

fCOPULA	representation for an S4 object of class "fCOPULA",
show	S4 print method.

Frechet Copulae:

pfrechetCopula

computes Frechet copula probability.

Usage

## S4 method for signature 'fCOPULA'
show(object)

pfrechetCopula(u = 0.5, v = u, type = c("m", "pi", "w"), 
    output = c("vector", "list"))

Arguments

object	[show] - an S4 object of class "fCOPULA".
output	[*frechetCopula] - 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	[*frechetCopula] - the type of the Frechet copula. A character string selected from: "m", "pi", or "w".
u, v	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.

Details

The function pfrechetCopula returns a numeric matrix of probabilities computed at grid positions u|v. The arguments u and v are two single values or two numeric vectors of the same length. If v is not specified then the same values are taken as for u. Alternatively, u may be given as a two column vector or as a list with two entries as vectors. The first column or entry is taken as u and the second as v.

Value

The print method show returns an S4 object of class "fCOPULA". The object contains the following slots:

@call	the function call.
@copula	the name of the copula.
@param	a list whose elements specify the model parameters of the copula.
@title	a character string with the name of the copula. This can be overwritten specifying a user defined input argument.
@description	a character string with an optional user defined description. By default just the current date will be returned.

The function pfrechetCopula returns a numeric vector of probabilities. An attribute named "control" is added which returns the name of the Frechet copula.

Author(s)

Diethelm Wuertz for the Rmetrics R-port.

Examples

## fCOPULA -
   getClass("fCOPULA")
   
## pfrechet -
   # The Frechet Copula - m:
   pfrechetCopula(0.5)
   pfrechetCopula(0.25, 0.75)
   pfrechetCopula(runif(5))
   
## grid2d - 
   grid2d()
   pfrechetCopula(grid2d())

fCopulae documentation built on Jan. 8, 2023, 1:10 a.m.