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

## Description

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

## Usage

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

## Arguments

 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).

## Details

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).

## Value

 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

## 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.

BiCopPDF, BiCopCDF, CDVineLogLik, CDVineSeqEst
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 ## 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]