sample_dvine() is a helper function that samples copula data from a given
D-vine copula. See details for more information on the parameterization of
the D-vine copula.
sample_dvine(
copula_par,
rotation_par,
copula_family1,
copula_family2 = copula_family1,
n
)A \(n \times 4\) matrix where each row corresponds to one sampled vector and the columns correspond to \(U_1\), \(U_2\), \(U_3\), and \(U_4\).
Parameter vector for the sequence of bivariate copulas that
define the D-vine copula. The elements of copula_par correspond to
\((c_{12}, c_{23}, c_{34}, c_{13;2}, c_{24;3}, c_{14;23})\).
Vector of rotation parameters for the sequence of
bivariate copulas that define the D-vine copula. The elements of
rotation_par correspond to \((c_{12}, c_{23}, c_{34}, c_{13;2},
c_{24;3}, c_{14;23})\).
Copula family of \(c_{12}\) and \(c_{34}\). For the
possible options, see loglik_copula_scale(). The elements of
copula_family correspond to \((c_{12}, c_{34})\).
Copula family of the other bivariate copulas. For the
possible options, see loglik_copula_scale(). The elements of
copula_family2 correspond to \((c_{23}, c_{13;2}, c_{24;3}, c_{14;23})\).
Number of samples to be taken from the D-vine copula.
Let \(\boldsymbol{U} = (U_1, U_2, U_3, U_4)'\) be a random vector with uniform margins. The corresponding distribution function is then a 4-dimensional copula. A D-vine copula as a family of \(k\)-dimensional copulas. Indeed, a D-vine copula is a \(k\)-dimensional copula that is constructed from a particular product of bivariate copula densities. In this function, only 4-dimensional copula densities are considered. Under the simplifying assumption, the 4-dimensional D-vine copula density is the product of the following bivariate copula densities:
\(c_{12}\), \(c_{23}\), and \(c_{34}\)
\(c_{13;2}\) and \(c_{24;3}\)
\(c_{14;23}\)