Distributacalcul (version 0.4.0)

bivariateCA: 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)

Value

Function :

• cBivariateCA returns the value of the copula.

• crBivariateCA returns simulated values of the copula.

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 : $$C(u_1,u_2)=u_1{u}_2^{1-\alpha }\times {\mathbf{\text{1}}}_{\{u_1\le u_2\}}+u_1^{1-\alpha }{u}_2\times {\mathbf{\text{1}}}_{\{u_1\ge u_2\}}$$ for $u_1,u_2,\alpha \in [0,1]$. It is the geometric mean of the independance and upper Fréchet bound copulas.

Examples

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

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