Public API

Core types

julia

AbstractVineCopula{p} <: Copulas.Copula{p}

Abstract supertype for all p-dimensional vine copula models implemented by VineCopulas.jl. Concrete subtypes include CVineCopula, DVineCopula, and RVineCopula.

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VineCopulas.VineCopula Type

julia

VineCopula

Alias for AbstractVineCopula.

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VineCopulas.PairCopula Type

julia

PairCopula

Alias for Copulas.Copula{2}. Pair-copulas are the bivariate building blocks used on vine edges.

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VineCopulas.CVineCopula Type

julia

CVineCopula(order, edges; trunc=length(order)-1)

Construct a canonical vine copula from a variable order and a triangular collection of bivariate pair-copulas. The entry edges[k][i] represents the pair-copula between the root order[k] and the child order[k+i], conditional on the previous roots order[1:k-1].

Matrices of observations follow the package convention p × n: rows are dimensions and columns are observations.

Example

julia

C12 = GaussianCopula([1.0 0.5; 0.5 1.0])
C13 = ClaytonCopula(2, 2.0)
C23_1 = FrankCopula(2, 3.0)
cv = CVineCopula([1, 2, 3], [[C12, C13], [C23_1]])

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VineCopulas.DVineCopula Type

julia

DVineCopula(order, edges; trunc=length(order)-1)

Construct a drawable/path vine copula from a variable order and a triangular collection of bivariate pair-copulas. The entry edges[k][i] represents the pair-copula between order[i] and order[i+k], conditional on the variables between them in the D-vine path.

Example

julia

C12 = GaussianCopula([1.0 0.5; 0.5 1.0])
C23 = ClaytonCopula(2, 2.0)
C13_2 = FrankCopula(2, 3.0)
dv = DVineCopula([1, 2, 3], [[C12, C23], [C13_2]])

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VineCopulas.RVineCopula Type

julia

RVineCopula(order, struct_array, edges; trunc=length(order)-1)
RVineCopula(matrix, edges)

Construct a regular-vine copula from an explicit structure array or from an R-vine matrix exchange representation. Standard general R-vine structures are validated against the proximity condition at construction time. General R-vine evaluation is covered by the external rvinecopulib correctness campaign.

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VineCopulas.RVineStructure Type

julia

RVineStructure(order, struct_array; trunc=length(order)-1)

Structure representation for a regular vine. It stores the variable order, triangular structure array, optional exchange matrix, and truncation level.

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VineCopulas.VineEdge Type

julia

VineEdge

Description of a pair-copula edge in a vine tree, including the conditioned variables, conditioning set, pair-copula, tree level, and within-tree index.

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Fitting family sets

VineCopulas.DEFAULT_PAIR_FAMILIES Constant

julia

DEFAULT_PAIR_FAMILIES

Stable parametric family set used by automatic pair-copula selection. It intentionally overlaps the common parametric core used in vinecopulib: Gaussian, Student-t, Clayton, Gumbel, Frank, Joe, BB1, BB6, BB7 and BB8. Independence is handled separately by include_independence=true.

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VineCopulas.ALL_PARAMETRIC_PAIR_FAMILIES Constant

julia

ALL_PARAMETRIC_PAIR_FAMILIES

Broader parametric set exposed by Copulas.jl/VineCopulas.jl. The default set is deliberately smaller because it is the set that should receive the strongest correctness and benchmark coverage first.

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Fitting is exposed through Distributions.fit, for example fit(PairCopula, U), fit(CVineCopula, U), fit(DVineCopula, U), and fit(RVineCopula, U).

Structure accessors

VineCopulas.order Function

julia

order(vine)

Return the variable order used by a vine copula.

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julia

order(vine)

Return the variable order used by a vine copula.

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Return the variable order used by an RVineCopula.

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VineCopulas.edges Function

julia

edges(vine)

Return the triangular array of bivariate pair-copulas used by a vine copula. Tree k is stored in edges(vine)[k].

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julia

edges(vine)

Return the triangular array of bivariate pair-copulas used by a vine copula. Tree k is stored in edges(vine)[k].

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Return the triangular array of pair-copulas used by an RVineCopula.

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VineCopulas.struct_array Function

julia

struct_array(vine)

Return the triangular structure array used by an RVineCopula.

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VineCopulas.truncation Function

julia

truncation(vine)

Return the number of active trees in the vine. A full p-dimensional vine has truncation level p - 1.

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julia

truncation(vine)

Return the number of active trees in the vine. A full p-dimensional vine has truncation level p - 1.

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Return the number of active trees in an RVineCopula.

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VineCopulas.rvine_matrix Function

julia

rvine_matrix(vc::RVineCopula)

Return an integer matrix representation of an RVineCopula. If the object was constructed from a matrix, a copy of that original matrix is returned; otherwise one is built from the stored structure array and order.

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Pair conditionals

VineCopulas.hfunc1 Function

julia

hfunc1(C, u, v)
hfunc1(C, U)

Compute for a bivariate pair-copula C. For an n × 2 matrix U, return one value per row.

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VineCopulas.hfunc2 Function

julia

hfunc2(C, u, v)
hfunc2(C, U)

Compute for a bivariate pair-copula C. For an n × 2 matrix U, return one value per row.

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VineCopulas.hinv1 Function

julia

hinv1(C, q, v)

Invert hfunc1 in its first coordinate: return u such that hfunc1(C, u, v) ≈ q. Singular copulas may use a generalized inverse.

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VineCopulas.hinv2 Function

julia

hinv2(C, q, u)

Invert hfunc2 in its second coordinate: return v such that hfunc2(C, u, v) ≈ q. Singular copulas may use a generalized inverse.

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VineCopulas.h₁ Function

Unicode alias for hfunc1.

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VineCopulas.h₂ Function

Unicode alias for hfunc2.

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VineCopulas.h₁⁻¹ Function

Unicode alias for hinv1.

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VineCopulas.h₂⁻¹ Function

Unicode alias for hinv2.

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Simulation and transforms

VineCopulas.simulate_qmc Function

julia

simulate_qmc(vine, N; randomized=true)

Generate N quasi-Monte Carlo observations from a vine copula using Sobol points followed by the inverse Rosenblatt transform. The returned matrix has size p × N, with rows corresponding to variables and columns to observations.

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VineCopulas.set_cdf_nsamples! Function

julia

set_cdf_nsamples!(N::Integer)

Set the global number of Monte Carlo or quasi-Monte Carlo samples used by the numerical cdf approximation for vine copulas. This does not affect pdf, logpdf, rand, or Rosenblatt transforms.

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VineCopulas.enable_deterministic_cdf! Function

julia

enable_deterministic_cdf!(Npow::Integer=15)

Use 2^Npow quasi-Monte Carlo points for the numerical cdf approximation. This helper is intended for reproducible examples and tests.

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Copulas.rosenblatt Function

julia

rosenblatt(vine, u)
rosenblatt(vine, U)

Compute the Rosenblatt transform of a point or matrix under a vine copula. A matrix input is interpreted as p × n: rows are dimensions and columns are observations. The output has the same shape as the input.

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VineCopulas.rosenblatt! Function

julia

rosenblatt!(out, vine, U)

In-place Rosenblatt transform. out and U must have the same p × n shape.

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Copulas.inverse_rosenblatt Function

julia

inverse_rosenblatt(vine, z)
inverse_rosenblatt(vine, Z)

Apply the inverse Rosenblatt transform. This maps independent uniforms on the unit hypercube into observations from the vine copula. Matrix inputs and outputs use the p × n convention.

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VineCopulas.inverse_rosenblatt! Function

julia

inverse_rosenblatt!(out, vine, Z)

In-place inverse Rosenblatt transform. out and Z must have the same p × n shape.

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Model summaries

VineCopulas.loglikelihood Function

julia

loglikelihood(vine, u)
loglikelihood(vine, U)

Return the log-density at a single point or the summed log-likelihood over a p × n matrix of observations.

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VineCopulas.npars Function

julia

npars(C)
npars(vine)

Return a lightweight structural parameter count. For pair-copulas this uses Distributions.params when available. For vines it sums over all active edges.

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VineCopulas.aic Function

julia