BiCopHfunc: Conditional distribution function (h-function) of a bivariate...
In CDVine: Statistical Inference of C- And D-Vine Copulas

Description Usage Arguments Details Value Author(s) References See Also Examples

This function evaluates the conditional distribution function (h-function) of a given parametric bivariate copula.

1	BiCopHfunc(u1, u2, family, par, par2=0)

`u1,u2`	Numeric vectors of equal length with values in [0,1].
`family`	An integer defining 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”) `14` = rotated Gumbel copula (180 degrees; “survival Gumbel”) `16` = rotated Joe copula (180 degrees; “survival Joe”) `17` = rotated BB1 copula (180 degrees; “survival BB1”) `18` = rotated BB6 copula (180 degrees; “survival BB6”) `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)
`par`	Copula parameter.
`par2`	Second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8; default: `par2 = 0`).

The h-function is defined as the conditional distribution function of a bivariate copula, i.e.,

h(u|v,θ) := F(u|v) = \partial C(u,v) / \partial v,

where C is a bivariate copula distribution function with parameter(s) θ. For more details see Aas et al. (2009).

`hfunc1`	Numeric vector of the conditional distribution function (h-function) evaluated at `u2` given `u1`, i.e., h(u2\|u1,θ).
`hfunc2`	Numeric vector of the conditional distribution function (h-function) evaluated at `u1` given `u2`, i.e., h(u1\|u2,θ).

Ulf Schepsmeier

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

BiCopPDF, BiCopCDF, CDVineLogLik, CDVineSeqEst

## Example 1: 4-dimensional C-vine model with mixed pair-copulas
data(worldindices)
Data = as.matrix(worldindices)[,1:4]
d = dim(Data)[2]
fam = c(5,1,3,14,3,2)

# sequential estimation
seqpar1 = CDVineSeqEst(Data,fam,type=1,method="itau")

# calculate the inputs of the second tree using h-functions
h1 = BiCopHfunc(Data[,1],Data[,2],fam[1],seqpar1$par[1])
h2 = BiCopHfunc(Data[,1],Data[,3],fam[2],seqpar1$par[2])
h3 = BiCopHfunc(Data[,1],Data[,4],fam[3],seqpar1$par[3])

# compare estimated parameters
BiCopEst(h1$hfunc1,h2$hfunc1,fam[4],method="itau")
seqpar1$par[4]

BiCopEst(h1$hfunc1,h3$hfunc1,fam[5],method="itau")
seqpar1$par[5]


## Example 2: 4-dimensional D-vine model with mixed pair-copulas

# sequential estimation
seqpar2 = CDVineSeqEst(Data,fam,type=2,method="itau")

# calculate the inputs of the second tree using h-functions
h1 = BiCopHfunc(Data[,1],Data[,2],fam[1],seqpar2$par[1])
h2 = BiCopHfunc(Data[,2],Data[,3],fam[2],seqpar2$par[2])
h3 = BiCopHfunc(Data[,3],Data[,4],fam[3],seqpar2$par[3])

# compare estimated parameters
BiCopEst(h1$hfunc2,h2$hfunc1,fam[4],method="itau")
seqpar2$par[4]

BiCopEst(h2$hfunc2,h3$hfunc1,fam[5],method="itau")
seqpar2$par[5]

The CDVine package is no longer developed actively.
Please consider using the more general VineCopula package
(see https://CRAN.R-project.org/package=VineCopula),
which extends and improves the functionality of CDVine.

For two parameter copulas the estimation method 'itau' cannot be used. The method is automatically set to 'mle'.
$par
[1] 1.239108

$par2
[1] 0

[1] 1.239108
$par
[1] 0.1655822

$par2
[1] 0

[1] 0.1655822
For two parameter copulas the estimation method 'itau' cannot be used. The method is automatically set to 'mle'.
$par
[1] 1.080577

$par2
[1] 0

[1] 1.080577
$par
[1] 0.2578596

$par2
[1] 0

[1] 0.2578596