Struct ArchimedeanCopula 

pub struct ArchimedeanCopula { /* private fields */ }

An exchangeable d-dimensional Archimedean copula with generator ψ_θ, sampled by Marshall and Olkin’s frailty method: draw a frailty V (whose Laplace transform is ψ), then d unit exponentials E_j, and return u_j = ψ(E_j / V).

Family	ψ(t)	Frailty V	θ	Kendall’s tau
Clayton	(1 + t)^(-1/θ)	Gamma(1/θ)	> 0	θ / (θ + 2)
Gumbel	exp(-t^(1/θ))	positive stable(1/θ)	>= 1	1 - 1/θ
Frank	-ln(1 - (1 - e^-θ) e^-t) / θ	logarithmic(1 - e^-θ)	> 0	1 + 4 (D_1(θ) - 1) / θ
Joe	1 - (1 - e^-t)^(1/θ)	Sibuya(1/θ)	>= 1	1 - 4 Σ_k 1 / (k (θk + 2)(θ(k - 1) + 2))

Clayton has lower-tail dependence 2^(-1/θ); Gumbel and Joe have upper-tail dependence 2 - 2^(1/θ); Frank has none. Draws use the frailty first, then the exponentials, all from the simulation’s stream.

use prospicio_core::StreamRng;
use prospicio_prob::copula::{Archimedean, ArchimedeanCopula, Copula};

// Clayton with tau = 0.5.
let c = ArchimedeanCopula::new(Archimedean::Clayton, 2.0, 3).unwrap();
let mut u = [0.0; 3];
c.sample(&mut StreamRng::new(1, 0), &mut u);
assert!(u.iter().all(|&x| x > 0.0 && x < 1.0));

Implementations

impl ArchimedeanCopula

pub fn new(family: Archimedean, theta: f64, dim: usize) -> Result<Self>

A dim-dimensional copula of family with parameter theta.

pub fn family(&self) -> Archimedean

pub fn theta(&self) -> f64

pub fn generator(&self, t: f64) -> f64

The generator ψ(t) for t >= 0.

Trait Implementations

impl Clone for ArchimedeanCopula

fn clone(&self) -> ArchimedeanCopula

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copula for ArchimedeanCopula

fn dim(&self) -> usize

Number of dimensions.

fn sample(&self, rng: &mut StreamRng, u: &mut [f64])

Fills u (length dim) with one draw of uniforms in (0, 1).

impl Debug for ArchimedeanCopula

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

Formats the value using the given formatter.

impl PartialEq for ArchimedeanCopula

fn eq(&self, other: &ArchimedeanCopula) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl StructuralPartialEq for ArchimedeanCopula