Supported pair-copula families

VineCopulas.jl uses bivariate copulas from Copulas.jl. A family is considered supported as a vine pair-copula when the following pieces are available and tested:

1. bivariate density/log-density,

2. hfunc1 and hfunc2,

3. hinv1 and hinv2 for simulation and inverse Rosenblatt transforms,

4. tests in the vine interface.

Current support table

Group	Family examples	Vine pair-copula status	Density path
Independence	IndependentCopula	Supported	Fast path
Elliptical	Gaussian	Supported and benchmark-oriented	Closed-form fast path
Elliptical	Student-t	Supported, correctness-oriented	Closed-form bivariate t copula path using scalar Student-t CDF/quantile routines
Archimedean one-parameter	Clayton, Frank, Gumbel, Joe	Supported	Closed form for Clayton/Frank/Gumbel; generator path for Joe
rvinecopulib BB families	BB1, BB6, BB7, BB8	Supported	Generator path with family-specific hooks
Additional Archimedean	AMH, Gumbel–Barnett, Inverse Gaussian, BB2, BB3, BB9, BB10	Supported by Copulas.jl integration	Generator path
Extreme-value	Logistic, Galambos, Hüsler–Reiss, Mixed, asymmetric tails, Marshall–Olkin, Cuadras–Augé, BC2, extreme-t	Supported/tested	Existing extreme-value path
Survival/rotated	SurvivalCopula wrappers	Supported when the base family has valid h-functions/inverses	Flip rules
Plackett, FGM, Raftery, M, W	Several miscellaneous Copulas.jl families	Not advertised as stable v0.1 vine families	Generic fallback
Empirical/Bernstein/Beta/Checkerboard	Nonparametric objects	Not part of stable v0.1 vine interface	Not targeted

The parametric family set overlapping with rvinecopulib is explicitly represented in the source layout: independence, Gaussian, Student-t, Clayton, Gumbel, Frank, Joe, BB1, BB6, BB7 and BB8. Nonparametric tll is not part of the stable v0.1 Julia interface.

Performance-oriented layout

Pair-copula methods are organized under src/PairCopulas/:

src/PairCopulas/
  Generic.jl
  Ellipticals/GaussianCopula.jl
  Ellipticals/TCopula.jl
  Archimedeans/ArchimedeanCopula.jl
  Archimedeans/ClaytonCopula.jl
  Archimedeans/GumbelCopula.jl
  Archimedeans/FrankCopula.jl
  Archimedeans/JoeCopula.jl
  Archimedeans/BB1Copula.jl
  Archimedeans/BB6Copula.jl
  Archimedeans/BB7Copula.jl
  Archimedeans/BB8Copula.jl
  ExtremeValue/ExtremeValueCopula.jl
  Miscellaneous/IndependentCopula.jl
  Miscellaneous/MiscellaneousCopulas.jl

This layout separates the generic vine engines from family-specific numerical primitives. The long-term development pattern is to add closed-form _pair_logpdf, hfunc1, hfunc2, hinv1, and hinv2 methods in the corresponding family file.

Why the table is conservative

It is not enough for a bivariate copula to have a density. Vine simulation requires inverse conditional distributions. A family should only be documented as fully supported after it passes pair-copula conditional tests and vine-level density/simulation tests.

Survival and rotations

Rotations are handled through Copulas.SurvivalCopula when the underlying base family has valid h-functions and inverse h-functions. The flip logic is implemented at the conditional level.