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

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.

## Value

Function :

• cBivariateCA returns the value of the copula.

• crBivariateCA returns simulated values of the copula.

## 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.

## Examples

cBivariateCA(u1 = .76, u2 = 0.4, dependencyParameter = 0.4)
#> [1] 0.3392721

crBivariateCA(numberSimulations = 10, seed = 42, dependencyParameter = 0.2)
#>            [,1]      [,2]
#>  [1,] 0.6873884 0.6873884
#>  [2,] 0.9876586 0.9876586
#>  [3,] 0.2130879 0.2130879
#>  [4,] 0.5539507 0.5539507
#>  [5,] 0.8003869 0.8003869
#>  [6,] 0.9264932 0.9264932
#>  [7,] 0.4470689 0.4470689
#>  [8,] 0.5148039 0.4646908
#>  [9,] 0.7352832 0.7352832
#> [10,] 0.5860752 0.5860752