Kendall's tau values of a vine copula model

Description

This function computes the values of Kendall's tau corresponding to the parameters of a C- or D-vine copula model.

Usage

1

Arguments

family

A d*(d-1)/2 integer vector of C-/D-vine pair-copula families with values
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

A d*(d-1)/2 vector of pair-copula parameters.

par2

A d*(d-1)/2 vector of second parameters for pair-copula families with two parameters (t, BB1, BB6, BB7, BB8; default: par2 = rep(0,length(family))).

Value

A d*(d-1)/2 vector of theoretical Kendall's tau values corresponding to the given pair-copula families and parameters.

Author(s)

Eike Brechmann

See Also

BiCopPar2Tau

Examples

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# specify the vine
fam3 = c(5,1,3,14,3,2)
par3 = c(0.9,0.3,0.2,1.1,0.2,0.7)
nu3 = c(0,0,0,0,0,7)

# compute the corresponding Kendall's tau values 
tau = CDVinePar2Tau(fam3,par3,nu3)

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