vinecopulib namespace

Tools for bivariate and vine copula modeling.

Namespaces

namespace bicop_families
Convenience definitions of sets of bivariate copula families.
namespace tools_select
namespace tools_stats
Utilities for statistical analysis.

Classes

class Bicop
A class for bivariate copula models.
class CVineStructure
A class for C-vine structures.
class DVineStructure
A class for D-vine structures.
class FitControlsBicop
A class for controlling fits of bivariate copula models.
struct FitControlsConfig
class FitControlsVinecop
A class for controlling fits of vine copula models.
class RVineStructure
A class for R-vine structures.
class RVineTrees
A list-of-trees decomposition of an R-vine structure.
template<typename T>
class TriangularArray
Triangular arrays.
class Vinecop
A class for vine copula models.

Enums

enum class BicopFamily { indep, gaussian, student, clayton, gumbel, frank, joe, bb1, bb6, bb7, bb8, tawn, tll }
A bivariate copula family identifier.

Typedefs

using TreeCriterionFunction = std::function<double(const Eigen::MatrixXd&, const Eigen::VectorXd&)>
A custom edge-weight function for vine structure selection.

Functions

auto get_family_name(BicopFamily family) -> std::string
Converts a BicopFamily into a string with its name.
auto get_family_enum(const std::string& family) -> BicopFamily
Converts a string name into a BicopFamily.
auto assemble_scores(Eigen::Index n, Eigen::Index p, const std::function<Eigen::VectorXd(Eigen::Index)>& col) -> Eigen::MatrixXd
Assembles an $ n \times p $ score matrix from a per-parameter column evaluator (col(k) returns column k). Shared by the fixed- and per-row-parameter scores() overloads so each keeps its own optimal logpdf_deriv() path (broadcast vs. per-row) while the loop lives once.
auto assemble_hessian(Eigen::Index p, const std::function<Eigen::VectorXd(Eigen::Index, Eigen::Index)>& col) -> Eigen::MatrixXd
Assembles the averaged, symmetric $ p \times p $ Hessian from a per- $ (a, b) $ second-derivative column evaluator (upper triangle only).
auto assemble_hessian_full(Eigen::Index n, Eigen::Index p, const std::function<Eigen::VectorXd(Eigen::Index, Eigen::Index)>& col) -> std::vector<Eigen::MatrixXd>
Assembles the per-observation, symmetric $ p \times p $ Hessians (one per row of u) from the same per- $ (a, b) $ column evaluator.
template<typename T>
auto operator<<(std::ostream& os, const TriangularArray<T>& tri_array) -> std::ostream&
Ostream method for TriangularArray, to be used with std::cout.
auto propagate_first_order(const Eigen::VectorXd& du1, const Eigen::VectorXd& du2, const Eigen::VectorXd& v1, const Eigen::VectorXd& v2) -> Eigen::VectorXd
auto operator<<(std::ostream& os, const RVineStructure& rvs) -> std::ostream&
Ostream method for RVineStructure, to be used with std::cout.

Enum documentation

enum class vinecopulib::BicopFamily
#include <vinecopulib/include/vinecopulib/bicop/family.hpp>

A bivariate copula family identifier.

The list below summarizes each family's parameter count, parameter range, available rotations, and tail-dependence behavior. The exact parameter bounds enforced at fit time are visible via Bicop::get_parameters_lower_bounds() / Bicop::get_parameters_upper_bounds(). The Kendall's-tau column refers to the closed-form mapping implemented by Bicop::parameters_to_tau() / Bicop::tau_to_parameters().

Enumerators
indep

Independence copula. 0 parameters; rotationless; no tail dependence; Kendall's tau is 0.
gaussian

Gaussian copula. 1 parameter (rho in (-1, 1)); rotationless; no tail dependence; Kendall's tau is (2 / pi) * arcsin(rho).
student

Student-t copula. 2 parameters (rho in (-1, 1), df > 2); rotationless; symmetric tail dependence; Kendall's tau is (2 / pi) * arcsin(rho).
clayton

Clayton copula. 1 parameter (theta > 0); rotations 0 / 90 / 180 / 270 degrees; lower-tail dependence; Kendall's tau is theta / (theta + 2).
gumbel

Gumbel copula (also extreme-value). 1 parameter (theta >= 1); rotations 0 / 90 / 180 / 270 degrees; upper-tail dependence; Kendall's tau is 1 - 1 / theta.
frank

Frank copula. 1 parameter (theta in R \ {0}); rotationless; no tail dependence; Kendall's tau given by the Debye-function form.
joe

Joe copula. 1 parameter (theta >= 1); rotations 0 / 90 / 180 / 270 degrees; upper-tail dependence; Kendall's tau via a series expansion.
bb1

BB1 copula (two-parameter Archimedean). 2 parameters (theta > 0, delta >= 1); rotations 0 / 90 / 180 / 270 degrees; both lower- and upper-tail dependence; Kendall's tau in closed form.
bb6

BB6 copula (two-parameter Archimedean). 2 parameters (theta >= 1, delta >= 1); rotations 0 / 90 / 180 / 270 degrees; upper-tail dependence; Kendall's tau in closed form.
bb7

BB7 copula (two-parameter Archimedean). 2 parameters (theta >= 1, delta > 0); rotations 0 / 90 / 180 / 270 degrees; both lower- and upper-tail dependence; Kendall's tau in closed form.
bb8

BB8 copula (two-parameter Archimedean). 2 parameters (theta >= 1, delta in (0, 1]); rotations 0 / 90 / 180 / 270 degrees; upper-tail dependence; Kendall's tau in closed form.
tawn

Tawn copula (extreme-value, asymmetric). 3 parameters; rotations 0 / 90 / 180 / 270 degrees; (asymmetric) upper-tail dependence; Kendall's tau via the Pickands dependence function.
tll

Transformation Local Likelihood (TLL) nonparametric estimator. No finite parametric form: the copula density is fit on a grid in the inverse-normal-transformed copula space. Data-driven rotation and tail behavior; Kendall's tau is rank-based on the fitted density.

Typedef documentation

using vinecopulib::TreeCriterionFunction = std::function<double(const Eigen::MatrixXd&, const Eigen::VectorXd&)>
#include <vinecopulib/include/vinecopulib/misc/fit_controls.hpp>

A custom edge-weight function for vine structure selection.

Maps a two-column matrix of pair-copula data and a vector of weights to a scalar dependence value. Used when tree_criterion is set to "custom". It is always called on the thread that starts the fit, so it need not be thread safe.

Function documentation

std::string vinecopulib::get_family_name(BicopFamily family)
#include <vinecopulib/include/vinecopulib/bicop/family.hpp>

Converts a BicopFamily into a string with its name.

Parameters
family The family.

BicopFamily vinecopulib::get_family_enum(const std::string& family)
#include <vinecopulib/include/vinecopulib/bicop/family.hpp>

Converts a string name into a BicopFamily.

Parameters
family The family name.

Eigen::MatrixXd vinecopulib::assemble_scores(Eigen::Index n, Eigen::Index p, const std::function<Eigen::VectorXd(Eigen::Index)>& col)
#include <vinecopulib/include/vinecopulib/bicop/implementation/class.ipp>

Assembles an $ n \times p $ score matrix from a per-parameter column evaluator (col(k) returns column k). Shared by the fixed- and per-row-parameter scores() overloads so each keeps its own optimal logpdf_deriv() path (broadcast vs. per-row) while the loop lives once.

Eigen::MatrixXd vinecopulib::assemble_hessian(Eigen::Index p, const std::function<Eigen::VectorXd(Eigen::Index, Eigen::Index)>& col)
#include <vinecopulib/include/vinecopulib/bicop/implementation/class.ipp>

Assembles the averaged, symmetric $ p \times p $ Hessian from a per- $ (a, b) $ second-derivative column evaluator (upper triangle only).

std::vector<Eigen::MatrixXd> vinecopulib::assemble_hessian_full(Eigen::Index n, Eigen::Index p, const std::function<Eigen::VectorXd(Eigen::Index, Eigen::Index)>& col)
#include <vinecopulib/include/vinecopulib/bicop/implementation/class.ipp>

Assembles the per-observation, symmetric $ p \times p $ Hessians (one per row of u) from the same per- $ (a, b) $ column evaluator.

#include <vinecopulib/include/vinecopulib/misc/triangular_array.hpp>
template<typename T>
std::ostream& vinecopulib::operator<<(std::ostream& os, const TriangularArray<T>& tri_array)

Ostream method for TriangularArray, to be used with std::cout.

Parameters
os An output stream.
tri_array A triangular array.

Eigen::VectorXd vinecopulib::propagate_first_order(const Eigen::VectorXd& du1, const Eigen::VectorXd& du2, const Eigen::VectorXd& v1, const Eigen::VectorXd& v2)
#include <vinecopulib/include/vinecopulib/vinecop/implementation/class.ipp>

first-order chain-rule push-forward of an argument perturbation through an h-function output: ∂h/∂u1 · v1 + ∂h/∂u2 · v2 (shared by the gradient cascade and the Hessian's hat/til propagations).

std::ostream& vinecopulib::operator<<(std::ostream& os, const RVineStructure& rvs)
#include <vinecopulib/include/vinecopulib/vinecop/rvine_structure.hpp>

Ostream method for RVineStructure, to be used with std::cout.

Parameters
os Output stream.
rvs R-vine structure array.