Struct OneFactorGaussianCopula 

pub struct OneFactorGaussianCopula { /* private fields */ }

One-factor Gaussian copula.

Models dependence through a single common factor Z and idiosyncratic terms. For each variable i: X_i = β_i * Z + sqrt(1 - β_i^2) * ε_i where Z, ε_i ~ N(0,1) are independent.

Bibliography

• Li, D. X. (2000). On default correlation: A copula function approach.

Implementations

impl OneFactorGaussianCopula

pub fn new(loadings: Vec<f64>) -> Result<Self>

Create a new one-factor Gaussian copula.

Arguments

• loadings - Factor loadings for each dimension (must be in [0, 1])

Returns

A new one-factor Gaussian copula

pub fn correlation(&self, i: usize, j: usize) -> Result<f64>

Get the implied correlation between dimensions i and j.

ρ_ij = β_i * β_j

pub fn correlation_matrix(&self) -> DMatrix<f64>

Get the correlation matrix implied by the factor loadings.

Trait Implementations

impl Clone for OneFactorGaussianCopula

fn clone(&self) -> OneFactorGaussianCopula

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copula for OneFactorGaussianCopula

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

Generate random samples from the copula.

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.

impl Debug for OneFactorGaussianCopula

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.