Package 'VC2copula'

Title: Extend the 'copula' Package with Families and Models from 'VineCopula'
Description: Provides new classes for (rotated) BB1, BB6, BB7, BB8, and Tawn copulas, extends the existing Gumbel and Clayton families with rotations, and allows to set up a vine copula model using the 'copula' API. Corresponding objects from the 'VineCopula' API can easily be converted.
Authors: Thomas Nagler [aut, cre], Benedikt Graeler [ctb]
Maintainer: Thomas Nagler <[email protected]>
License: GPL-3
Version: 0.1.5
Built: 2025-01-29 04:38:49 UTC
Source: https://github.com/tnagler/vc2copula

Help Index

Constructors for BB1 copulas

Description

Constructs an object of the BB1Copula (survival sur, 90 degree rotated r90 and 270 degree rotated r270) family for given parameters.

Usage

BB1Copula(param = c(1, 1))

surBB1Copula(param = c(1, 1))

r90BB1Copula(param = c(-1, -1))

r270BB1Copula(param = c(-1, -1))

Arguments

param

The parameter param defines the copula through theta and delta.

Value

One of the respective BB1 copula classes (BB1Copula, surBB1Copula, r90BB1Copula, r270BB1Copula).

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.

See Also

See also BB6Copula(), BB7Copula(), BB8Copula() and joeCopula() for further wrapper functions to the VineCopula-package().

Examples

library(copula)

persp(BB1Copula(c(1, 1.5)), dCopula, zlim = c(0, 10))
persp(surBB1Copula(c(1, 1.5)), dCopula, zlim = c(0, 10))
persp(r90BB1Copula(c(-1, -1.5)), dCopula, zlim = c(0, 10))
persp(r270BB1Copula(c(-1, -1.5)), dCopula, zlim = c(0, 10))

BB1 copula models

Description

Wrapper classes representing the BB1, survival BB1, 90 degree and 270 degree rotated BB1 copula families (Joe 1997) from VineCopula-package().

Objects from the Classes

Objects can be created by calls of the form new("BB1Copula", ...), new("surBB1Copula", ...), new("r90BB1Copula", ...) and new("r270BB1Copula", ...) or by the functions BB1Copula(), surBB1Copula(), r90BB1Copula() and r270BB1Copula().

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.

See Also

See also BB6Copula, BB7Copula, BB8Copula and joeCopula for further wrapper classes to the VineCopula-package().

Examples

showClass("BB1Copula")

Constructors for BB6 copulas

Description

Constructs an object of the BB6Copula (survival sur, 90 degree rotated r90 and 270 degree rotated r270) family for given parameters.

Usage

BB6Copula(param = c(1, 1))

surBB6Copula(param = c(1, 1))

r90BB6Copula(param = c(-1, -1))

r270BB6Copula(param = c(-1, -1))

Arguments

param

The parameter param defines the copula through theta and delta.

Value

One of the respective BB6 copula classes (BB6Copula, surBB6Copula, r90BB6Copula, r270BB6Copula).

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.

See Also

See also BB6Copula(), BB7Copula(), BB8Copula() and joeCopula() for further wrapper functions to the VineCopula-package().

Examples

library(copula)

persp(BB6Copula(c(1, 1.5)), dCopula, zlim = c(0, 10))
persp(surBB6Copula(c(1, 1.5)), dCopula, zlim = c(0, 10))
persp(r90BB6Copula(c(-1, -1.5)), dCopula, zlim = c(0, 10))
persp(r270BB6Copula(c(-1, -1.5)), dCopula, zlim = c(0, 10))

BB6 copula models

Description

Wrapper classes representing the BB6, survival BB6, 90 degree and 270 degree rotated BB6 copula families (Joe 1997) from VineCopula-package().

Objects from the Classes

Objects can be created by calls of the form new("BB6Copula", ...), new("surBB6Copula", ...), new("r90BB6Copula", ...) and new("r270BB6Copula", ...) or by the functions BB6Copula(), surBB6Copula(), r90BB6Copula() and r270BB6Copula().

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.

See Also

See also BB6Copula, BB7Copula, BB8Copula and joeCopula for further wrapper classes to the VineCopula-package().

Examples

showClass("BB6Copula")

Constructors for BB7 copulas

Description

Constructs an object of the BB7Copula (survival sur, 90 degree rotated r90 and 270 degree rotated r270) family for given parameters.

Usage

BB7Copula(param = c(1, 1))

surBB7Copula(param = c(1, 1))

r90BB7Copula(param = c(-1, -1))

r270BB7Copula(param = c(-1, -1))

Arguments

param

The parameter param defines the copula through theta and delta.

Value

One of the respective BB7 copula classes (BB7Copula, surBB7Copula, r90BB7Copula, r270BB7Copula).

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.

See Also

See also BB6Copula(), BB7Copula(), BB8Copula() and joeCopula() for further wrapper functions to the VineCopula-package().

Examples

library(copula)

persp(BB7Copula(c(1, 1.5)), dCopula, zlim = c(0, 10))
persp(surBB7Copula(c(1, 1.5)), dCopula, zlim = c(0, 10))
persp(r90BB7Copula(c(-1, -1.5)), dCopula, zlim = c(0, 10))
persp(r270BB7Copula(c(-1, -1.5)), dCopula, zlim = c(0, 10))

BB7 copula models

Description

Wrapper classes representing the BB7, survival BB7, 90 degree and 270 degree rotated BB7 copula families (Joe 1997) from VineCopula-package().

Objects from the Classes

Objects can be created by calls of the form new("BB7Copula", ...), new("surBB7Copula", ...), new("r90BB7Copula", ...) and new("r270BB7Copula", ...) or by the functions BB7Copula(), surBB7Copula(), r90BB7Copula() and r270BB7Copula().

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.

See Also

See also BB7Copula, BB7Copula, BB8Copula and joeCopula for further wrapper classes to the VineCopula-package().

Examples

showClass("BB7Copula")

Constructors for BB8 copulas

Description

Constructs an object of the BB8Copula (survival sur, 90 degree rotated r90 and 270 degree rotated r270) family for given parameters.

Usage

BB8Copula(param = c(1, 1))

surBB8Copula(param = c(1, 1))

r90BB8Copula(param = c(-1, -1))

r270BB8Copula(param = c(-1, -1))

Arguments

param

The parameter param defines the copula through theta and delta.

Value

One of the respective BB8 copula classes (BB8Copula, surBB8Copula, r90BB8Copula, r270BB8Copula).

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.

See Also

See also BB6Copula(), BB7Copula(), BB8Copula() and joeCopula() for further wrapper functions to the VineCopula-package().

Examples

library(copula)

persp(BB8Copula(c(2, 0.9)), dCopula, zlim = c(0, 10))
persp(surBB8Copula(c(2, 0.9)), dCopula, zlim = c(0, 10))
persp(r90BB8Copula(c(-2, -0.9)), dCopula, zlim = c(0, 10))
persp(r270BB8Copula(c(-2, -0.9)), dCopula, zlim = c(0, 10))

BB8 copula models

Description

Wrapper classes representing the BB8, survival BB8, 90 degree and 270 degree rotated BB8 copula families (Joe 1997) from VineCopula-package().

Objects from the Classes

Objects can be created by calls of the form new("BB8Copula", ...), new("surBB8Copula", ...), new("r90BB8Copula", ...) and new("r270BB8Copula", ...) or by the functions BB8Copula(), surBB8Copula(), r90BB8Copula() and r270BB8Copula().

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.

See Also

See also BB8Copula, BB8Copula, BB8Copula and joeCopula for further wrapper classes to the VineCopula-package().

Examples

showClass("BB8Copula")

Construction of a Copula Object from a VineCopula Family Index

Description

A VineCopula family index along with its parameters is used to construct a corresponding copula object.

Usage

BiCop2copula(family, par, par2 = 0, obj = NULL)

copulaFromFamilyIndex(family, par, par2 = 0)

Arguments

family

a family index as defined in VineCopula-package().
par

first parameter.
par2

second parameter.
obj

BiCop() object containing the family and parameter specification.

Details

If the family and parameter specification is stored in a ⁠[BiCop()]⁠ object obj, the alternative version 

BiCop2copula(u1, u2, obj)

can be used.

Value

An object inheriting copula corresponding to the specific family.

Examples

# normalCopula with parameter 0.5
BiCop2copula(1, 0.5)

# rotated Tawn T2 copula
BiCop2copula(224, -2, 0.5)

Partial Derivatives of Copulas

Description

Similar to dCopula() and pCopula() the function dduCopula evaluates the partial derivative ∂∂uC(u,v)\frac{\partial}{\partial u} C(u,v) and the function ddvCopula evaluates the partial derivative ∂∂vC(u,v)\frac{\partial}{\partial v} C(u,v) of the provided copula.

Usage

dduCopula(u, copula, ...)

## S4 method for signature 'matrix,normalCopula'
dduCopula(u, copula)

## S4 method for signature 'numeric,normalCopula'
dduCopula(u, copula, ...)

## S4 method for signature 'matrix,normalCopula'
ddvCopula(u, copula)

## S4 method for signature 'numeric,normalCopula'
ddvCopula(u, copula, ...)

## S4 method for signature 'matrix,tCopula'
dduCopula(u, copula)

## S4 method for signature 'numeric,tCopula'
dduCopula(u, copula, ...)

## S4 method for signature 'matrix,tCopula'
ddvCopula(u, copula)

## S4 method for signature 'numeric,tCopula'
ddvCopula(u, copula, ...)

## S4 method for signature 'matrix,gumbelCopula'
dduCopula(u, copula)

## S4 method for signature 'numeric,gumbelCopula'
dduCopula(u, copula, ...)

## S4 method for signature 'matrix,gumbelCopula'
ddvCopula(u, copula)

## S4 method for signature 'numeric,gumbelCopula'
ddvCopula(u, copula, ...)

## S4 method for signature 'matrix,claytonCopula'
dduCopula(u, copula)

## S4 method for signature 'numeric,claytonCopula'
dduCopula(u, copula, ...)

## S4 method for signature 'matrix,claytonCopula'
ddvCopula(u, copula)

## S4 method for signature 'numeric,claytonCopula'
ddvCopula(u, copula, ...)

## S4 method for signature 'matrix,indepCopula'
dduCopula(u, copula)

## S4 method for signature 'numeric,indepCopula'
dduCopula(u, copula, ...)

## S4 method for signature 'matrix,indepCopula'
ddvCopula(u, copula)

## S4 method for signature 'numeric,indepCopula'
ddvCopula(u, copula, ...)

## S4 method for signature 'matrix,frankCopula'
dduCopula(u, copula)

## S4 method for signature 'numeric,frankCopula'
dduCopula(u, copula, ...)

## S4 method for signature 'matrix,frankCopula'
ddvCopula(u, copula)

## S4 method for signature 'numeric,frankCopula'
ddvCopula(u, copula, ...)

Arguments

u

Pairs of values for which the partial derivative should be evaluated.
copula

The copula object representing the family member of interest.
...

additional arguments can be passed on to the underlying functions.

Value

A vector of the evaluated partial derivatives of the same length as rows in u.

Examples

library(copula)

BB1Cop <- BB1Copula()
BB1CopSmpl <- rCopula(100, BB1Cop)

# conditional probabilities of a Gaussian copula given u
BB1GivenU <- dduCopula(BB1CopSmpl, BB1Cop)

# vs. conditional probabilities of a Gaussian copula given v
BB1GivenV <- ddvCopula(BB1CopSmpl[, c(2, 1)], BB1Cop)

plot(BB1GivenU, BB1GivenV)
abline(0, 1)

A dedicated method to use the estimation routines from the VineCopula package

Description

Bivariate copulas are estimated based on BiCopEst and vine copulas through RVineStructureSelect or RVineCopSelect depending on the method argument.

Usage

BCfitCopula(copula, data, method = "ml")

Arguments

copula

an object of the desired copula class
data

a matrix holding the U(0,1) distributed data columns
method

for BIVARIATE copulas either "ml" or "itau" for maximum likelihood estimation or inverse tau estimation (for one parameter families) respectively. See BiCopEst for details. In case of a VINE copulas a list with names entries StructureSelect (default: FALSE), indeptest (default: FALSE), familyset (default: 'NA') and indeptest (default: FALSE). See RVineStructureSelect or RVineCopSelect for details.

Value

an object of class fitCopula as in the copula package.

Examples

u <- rCopula(1000, tawnT1Copula(c(3, 0.5)))

fitCopula(tawnT1Copula(), u)

Constructors for Joe copulas

Description

Constructs an object of the (survival surJoeBiCopula, 90 degree rotated r90JoeBiCopula and 270 degree rotated r270JoeBiCopula) family for a given parameter. Note that package copula-package() provides a class joeCopula as well.

Usage

joeBiCopula(param = 2)

surJoeBiCopula(param = 2)

r90JoeBiCopula(param = -2)

r270JoeBiCopula(param = -2)

Arguments

param

The parameter param defines the copula through theta.

Value

One of the respective Joe copula classes (joeBiCopula, surJoeBiCopula, r90JoeBiCopula, r270JoeBiCopula).

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.

See Also

See also BB1Copula(), BB6Copula(), BB7Copula() and BB8Copula() for further wrapper functions to the VineCopula-package().

Examples

library(copula)

persp(surJoeBiCopula(1.5), dCopula, zlim = c(0, 10))
persp(r90JoeBiCopula(-1.5), dCopula, zlim = c(0, 10))
persp(r270JoeBiCopula(-1.5), dCopula, zlim = c(0, 10))

Joe copula models

Description

Wrapper classes representing the bivariate Joe, survival Joe, 90 degree and 270 degree rotated Joe copula families (Joe 1997) from VineCopula-package(). Note that package copula-package() provides a class joeCopula as well.

Objects from the Classes

Objects can be created by calls of the form new("joeBiCopula", ...), new("surJoeBiCopula", ...), new("r90JoeBiCopula", ...) and new("r270JoeBiCopula", ...) or by the functions joeBiCopula(), surJoeBiCopula(), r90JoeBiCopula() and r270JoeBiCopula().

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.

See Also

See also BB1Copula, BB6Copula, BB7Copula and BB8Copula for further wrapper classes to the VineCopula-package().

Examples

showClass("surJoeBiCopula")

Constructors for survival and rotated Clayton Copulas

Description

These are wrappers to functions from VineCopula-package()

Usage

surClaytonCopula(param = 1)

r90ClaytonCopula(param = -1)

r270ClaytonCopula(param = -1)

Arguments

param

A single parameter defining the Copula.

Value

An object of class surClaytonCopula, r90ClaytonCopula or r270ClaytonCopula respectively.

Examples

library(copula)

persp(surClaytonCopula(1.5), dCopula, zlim = c(0, 10))
persp(r90ClaytonCopula(-1.5), dCopula, zlim = c(0, 10))
persp(r270ClaytonCopula(-1.5), dCopula, zlim = c(0, 10))

Survival and rotated Clayton copula models

Description

A class representing rotated versions of the Clayton copula family (survival, 90 and 270 degree rotated).

Objects from the Class

Objects can be created by calls of the form new("surClaytonCopula", ...), new("r90ClaytonCopula", ...) and new("r270ClaytonCopula", ...) or by the function surClaytonCopula(), r90ClaytonCopula() and r270ClaytonCopula() respectively.

See Also

VineCopula-package()

Examples

library(copula)

persp(surClaytonCopula(.5), dCopula, zlim = c(0, 10))
persp(r90ClaytonCopula(-.5), dCopula, zlim = c(0, 10))
persp(r270ClaytonCopula(-.5), dCopula, zlim = c(0, 10))

Constructors for survival and rotated Gumbel Copulas

Description

These are wrappers to functions from VineCopula-package()

Usage

surGumbelCopula(param = 1)

r90GumbelCopula(param = -1)

r270GumbelCopula(param = -1)

Arguments

param

A single parameter defining the Copula.

Value

An object of class surGumbelCopula, r90GumbelCopula or r270GumbelCopula respectively.

Examples

library(copula)

persp(surGumbelCopula(1.5), dCopula, zlim = c(0, 10))
persp(r90GumbelCopula(-1.5), dCopula, zlim = c(0, 10))
persp(r270GumbelCopula(-1.5), dCopula, zlim = c(0, 10))

Survival and rotated Gumbel copula models

Description

A class representing rotated versions of the Gumbel copula family (survival, 90 and 270 degree rotated).

Objects from the Class

Objects can be created by calls of the form new("surGumbelCopula", ...), new("r90GumbelCopula", ...) and new("r270GumbelCopula", ...) or by the function surGumbelCopula(), r90GumbelCopula() and r270GumbelCopula() respectively.

See Also

VineCopula-package()

Examples

library(copula)

persp(surGumbelCopula(5), dCopula, zlim = c(0, 10))
persp(r90GumbelCopula(-5), dCopula, zlim = c(0, 10))
persp(r270GumbelCopula(-5), dCopula, zlim = c(0, 10))

Constructor for Tawn copulas (type 1)

Description

Constructs an object of the tawnT1Copula (survival sur, 90 degree rotated r90 and 270 degree rotated r270) family for given parameters.

Usage

tawnT1Copula(param = c(2, 0.5))

surTawnT1Copula(param = c(2, 0.5))

r90TawnT1Copula(param = c(-2, 0.5))

r270TawnT1Copula(param = c(-2, 0.5))

Arguments

param

The parameter param defines the copula through param1 and param2.

Value

One of the Tawn type 1 copula classes (tawnT1Copula, surTawnT1Copula, r90TawnT1Copula, r270TawnT1Copula).

See Also

tawnT1Copula() and the package VineCopula-package() for implementation details.

Examples

library(copula)

persp(tawnT1Copula(), dCopula, zlim = c(0, 10))
persp(surTawnT1Copula(), dCopula, zlim = c(0, 10))
persp(r90TawnT1Copula(), dCopula, zlim = c(0, 10))
persp(r270TawnT1Copula(), dCopula, zlim = c(0, 10))

Tawn copula models (type 1)

Description

S4-class representation of the Tawn Copula family of type 1 and rotated versions there of.

Objects from the Class

Objects can be created by calls of the form new("tawnT1Copula", ...), or through the explicit constructors tawnT1Copula(), surTawnT1Copula(), r90TawnT1Copula() and r270TawnT1Copula() respectively.

See Also

tawnT1Copula and the package VineCopula-package() for implementation details.

Examples

showClass("tawnT1Copula")

Constructor for Tawn copulas (type 2)

Description

Constructs an object of the tawnT2Copula (survival sur, 90 degree rotated r90 and 270 degree rotated r270) family for given parameters.

Usage

tawnT2Copula(param = c(2, 0.5))

surTawnT2Copula(param = c(2, 0.5))

r90TawnT2Copula(param = c(-2, 0.5))

r270TawnT2Copula(param = c(-2, 0.5))

Arguments

param

The parameter param defines the copula through param1 and param2.

Value

One of the Tawn type 2 copula classes (tawnT2Copula, surTawnT2Copula, r90TawnT2Copula, r270TawnT2Copula).

See Also

tawnT2Copula() and the package VineCopula-package() for implementation details.

Examples

library(copula)

persp(tawnT2Copula(), dCopula, zlim = c(0, 10))
persp(surTawnT2Copula(), dCopula, zlim = c(0, 10))
persp(r90TawnT2Copula(), dCopula, zlim = c(0, 10))
persp(r270TawnT2Copula(), dCopula, zlim = c(0, 10))

Tawn copula models (type 2)

Description

S4-class representation of the Tawn Copula family of type 2 and rotated versions there of.

Objects from the Class

Objects can be created by calls of the form new("tawnT2Copula", ...), or through the explicit constructors tawnT2Copula(), surTawnT2Copula(), r90TawnT2Copula() and r270TawnT2Copula() respectively.

See Also

tawnT2Copula and the package VineCopula-package() for implementation details.

Examples

showClass("tawnT2Copula")

Constructor of the Class vineCopula.

Description

Constructs an instance of the vineCopula class.

Usage

vineCopula(RVM, type = "CVine")

Arguments

RVM

An object of class RVineMatrix generated from RVineMatrix in the package VineCopula-package or an integer (e.g. 4L) defining the dimension (an independent Gaussian C-vine of this dimension will be constructed).
type

A predefined type if only the dimension is provided and ignored otherwise, the default is a canonical vine

Value

An instance of the vineCopula class.

Author(s)

Benedikt Graeler

References

Aas, K., C. Czado, A. Frigessi, and H. Bakken (2009). Pair-copula constructions of multiple dependence Insurance: Mathematics and Economics 44 (2), 182-198.

Examples

# a C-vine of independent copulas
vine <- vineCopula(4L, "CVine")

library(copula)
library(lattice)

cloud(V1 ~ V2 + V3, as.data.frame(rCopula(500, vine)))

Class "vineCopula"

Description

A class representing vine copulas in a object oriented implementations. Many functions go back to the package VineCopula-package

Objects from the Class

Objects can be created by calls of the form new("vineCopula", ...) or through the function vineCopula.

Author(s)

Benedikt Graeler

References

Aas, K., C. Czado, A. Frigessi, and H. Bakken (2009). Pair-copula constructions of multiple dependence Insurance: Mathematics and Economics 44 (2), 182-198.

See Also

RVineMatrix from package VineCopula-package

Examples

showClass("vineCopula")