Copula families

[tnagler]

HuEach copula family is implemented as a class inheriting from the base class Bicop. For each virtual method of Bicop a family specific method has to be implemented.

1. Elliptical families bicop_elliptical.cpp, bicop_elliptical.hpp

• Gaussian bicop_normal.cpp, bicop_normal.hpp
• Student t bicop_student.cpp, bicop_student.hpp

2. Archimedean families bicop_archimedean.cpp, bicop_archimedean.hpp

• Clayton bicop_clayton.cpp, bicop_clayton.hpp
• Gumbel bicop_gumbel.cpp, bicop_gumbel.hpp
• Frank bicop_frank.cpp, bicop_frank.hpp
• Joe bicop_joe.cpp, bicop_joe.hpp
• BB families

3. Other parameteric families

• Tawns

4. Nonparameteric methods

• Transformation kernel
• Bernstein copula

[tvatter]

I would add:

3. Archimedean:

• Ali-Mikhail-Haq

4. Extreme-value

• Husler-Reiss
• Galambos
• t-EV

5. Other parametric families

• Plackett
• Farlie-Gumbel-Morgenstern

[tnagler]

I want to add: 2/4-part rotation-mixtures, e..g., a mixture of Gumbel 0°,90°,180°,270°. They're especially useful for time series models I think (the implicit copula of a GARCH looks like such mixture of Gumbels).

This triggers a some related issues:

• How can we make the library more extensible regarding families? Optimtally, a project depending on vinecopulib could implement new families and use it in any of the other functions (sim/pdf/etc).
• The more families we add, the less unreasonable it is to have "bicop_families:all" as a default. Idea: Create a few sensible collections, like "Thibault's favorites", "Thomas' favorites", "Time series", "Symmmetric", ...? Sillt: what's a good default?
• We should really change our default selcrict to aic. It's my fault that we have bic, but it makes absolutely no sense when we have nonparametric families (even otherwise).