bivariateCA {Distributacalcul}

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)