bivariateCA: Bivariate Cuadras-Augé Copula

In Distributacalcul: Probability Distribution Functions

Bivariate Cuadras-Augé Copula

Description

Computes CDF and simulations of the bivariate Cuadras-Augé copula.

Usage

cBivariateCA(u1, u2, dependencyParameter, ...)

crBivariateCA(numberSimulations = 10000, seed = 42, dependencyParameter)

Arguments

u1, u2	points at which to evaluate the copula.
dependencyParameter	correlation parameter.
...	other parameters.
numberSimulations	Number of simulations.
seed	Simulation seed, 42 by default.

Details

The bivariate Cuadras-Augé copula has CDF :

C(u_{1}, u_{2}) = u_{1}u_{2}^{1 - \alpha} \times% \textbf{1}_{\{u_{1} \leq u_{2}\}} + u_{1}^{1 - \alpha}u_{2} \times% \textbf{1}_{\{u_{1} \geq u_{2}\}}

for u_{1}, u_{2}, \alpha \in [0, 1]. It is the geometric mean of the independance and upper Fréchet bound copulas.

Value

Function :

• cBivariateCA returns the value of the copula.

• crBivariateCA returns simulated values of the copula.

Examples

cBivariateCA(u1 = .76, u2 = 0.4, dependencyParameter = 0.4)

crBivariateCA(numberSimulations = 10, seed = 42, dependencyParameter = 0.2)

Distributacalcul documentation built on May 29, 2024, 9:25 a.m.