CopulaeClass: Bivariate Copulae 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:

ll{ fCOPULA representation for an S4 object of class "fCOPULA", show S4 print method. } Frechet Copulae: ll{ pfrechetCopula computes Frechet copula probability. }

Usage

## S3 method for class '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

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

Value

The print method show returns an S4 object of class "fCOPULA". The object contains the following slots:
@callthe function call.
@copulathe name of the copula.
@parama list whose elements specify the model parameters of the copula.
@titlea character string with the name of the copula. This can be overwritten specifying a user defined input argument.
@descriptiona 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.

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.

Examples

Run this code

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