Struct DVineCopula 

pub struct DVineCopula { /* private fields */ }

D-vine copula (Drawable vine).

In a D-vine, each tree has a path structure. Tree 1: copulas C_{j,j+1} for j=1,…,d-1 Tree 2: copulas C_{j,j+2|j+1} for j=1,…,d-2 etc.

Example Structure (4D)

Tree 1: C_{12}, C_{23}, C_{34} Tree 2: C_{13|2}, C_{24|3} Tree 3: C_{14|23}

Implementations

impl DVineCopula

pub fn new(dimension: usize, trees: Vec<Vec<PairCopula>>) -> Result<Self>

Create a new D-vine copula.

Arguments

• dimension - Number of dimensions
• trees - Vector of trees, each containing pair-copulas

Returns

A new D-vine copula

Trait Implementations

impl Clone for DVineCopula

fn clone(&self) -> DVineCopula

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copula for DVineCopula

fn sample<R: Rng + ?Sized>(&self, n: usize, rng: &mut R) -> Result<DMatrix<f64>>

Sample by inverting the Rosenblatt transform (Aas et al., 2009, Algorithm 2).

Two tables of conditional distribution values are kept, indexed by variable j and by k, the size of the conditioning set plus one:

• fwd[j][k] = F(x_j | x_{j-k+1}, …, x_{j-1})
• bwd[j][k] = F(x_j | x_{j+1}, …, x_{j+k-1})

with fwd[j][1] = bwd[j][1] = u_j. They satisfy

• fwd[i][k+1] = h(fwd[i][k] | bwd[i-k][k]) using trees[k-1][i-k]
• bwd[j][k+1] = h(bwd[j][k] | fwd[j+k][k]) using trees[k-1][j]

Variable i is drawn by setting fwd[i][i+1] = w[i] and inverting the first recursion down to fwd[i][1]; the second recursion then extends bwd for the variables that follow.

fn cdf(&self, u: &[f64]) -> Result<f64>

Evaluate the copula cumulative distribution function (CDF) at point u.

fn pdf(&self, u: &[f64]) -> Result<f64>

Evaluate the copula probability density function (PDF) at point u.

fn dimension(&self) -> usize

Get the dimension of the copula.

fn conditional_cdf(&self, u: &[f64], given: &[usize]) -> Result<f64>

Compute the conditional copula CDF given some variables.

fn tail_dependence(&self) -> Result<(f64, f64)>

Compute the tail dependence coefficients.

fn kendall_tau(&self) -> Result<f64>

Compute Kendall’s tau for this copula.

fn spearman_rho(&self) -> Result<f64>

Compute Spearman’s rho for this copula.

fn has_closed_form(&self) -> (bool, bool)

Check if the copula has analytical forms for CDF and PDF.

fn family_name(&self) -> &'static str

Get a string identifier for the copula family.