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BiCopCDF

Distribution Function of a Bivariate Copula

Description

This function evaluates the cumulative distribution function (CDF) of a given parametric bivariate copula.

Usage

BiCopCDF(u1, u2, family, par, par2 = 0, obj = NULL, check.pars = TRUE)

Arguments

u1, u2

numeric vectors of equal length with values in [0,1].
family

integer; single number or vector of size length(u1); defines the bivariate copula family:
0 = independence copula
1 = Gaussian copula
2 = Student t copula (t-copula)
3 = Clayton copula
4 = Gumbel copula
5 = Frank copula
6 = Joe copula
7 = BB1 copula
8 = BB6 copula
9 = BB7 copula
10 = BB8 copula
13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
20 = rotated BB8 copula (180 degrees; “survival BB8”)
23 = rotated Clayton copula (90 degrees)
'24' = rotated Gumbel copula (90 degrees)
'26' = rotated Joe copula (90 degrees)
'27' = rotated BB1 copula (90 degrees)
'28' = rotated BB6 copula (90 degrees)
'29' = rotated BB7 copula (90 degrees)
'30' = rotated BB8 copula (90 degrees)
'33' = rotated Clayton copula (270 degrees)
'34' = rotated Gumbel copula (270 degrees)
'36' = rotated Joe copula (270 degrees)
'37' = rotated BB1 copula (270 degrees)
'38' = rotated BB6 copula (270 degrees)
'39' = rotated BB7 copula (270 degrees)
'40' = rotated BB8 copula (270 degrees)
'104' = Tawn type 1 copula
'114' = rotated Tawn type 1 copula (180 degrees)
'124' = rotated Tawn type 1 copula (90 degrees)
'134' = rotated Tawn type 1 copula (270 degrees)
'204' = Tawn type 2 copula
'214' = rotated Tawn type 2 copula (180 degrees)
'224' = rotated Tawn type 2 copula (90 degrees)
'234' = rotated Tawn type 2 copula (270 degrees)

par

numeric; single number or vector of size length(u1); copula parameter.
par2

numeric; single number or vector of size length(u1); second parameter for bivariate copulas with two parameters (BB1, BB6, BB7, BB8, Tawn type 1 and type 2; default: par2 = 0).
obj

BiCop object containing the family and parameter specification.
check.pars

logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

Details

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

BiCopCDF(u1, u2, obj)

can be used.

Value

A numeric vector of the bivariate copula distribution function

  • of the copula family

  • with parameter(s) par, par2

  • evaluated at u1 and u2.

Note

The calculation of the cumulative distribution function (CDF) of the Student's t copula (family = 2) is only approximate. For numerical reasons, the degree of freedom parameter (par2) is rounded to an integer before calculation of the CDF.

Author(s)

Eike Brechmann

See Also

Examples

## simulate from a bivariate Clayton copula
set.seed(123)
cop <- BiCop(family = 3, par = 3.4)
simdata <- BiCopSim(300, cop)

## evaluate the distribution function of the bivariate Clayton copula
u1 <- simdata[,1]
u2 <- simdata[,2]
BiCopCDF(u1, u2, cop)

## select a bivariate copula for the simulated data
cop <- BiCopSelect(u1, u2)
summary(cop)
## and evaluate its CDF
BiCopCDF(u1, u2, cop)
VineCopula

Statistical Inference of Vine Copulas

v2.4.1
GPL (>= 2)
Authors
Thomas Nagler [aut, cre], Ulf Schepsmeier [aut], Jakob Stoeber [aut], Eike Christian Brechmann [aut], Benedikt Graeler [aut], Tobias Erhardt [aut], Carlos Almeida [ctb], Aleksey Min [ctb, ths], Claudia Czado [ctb, ths], Mathias Hofmann [ctb], Matthias Killiches [ctb], Harry Joe [ctb], Thibault Vatter [ctb]
Initial release

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