Computes CDF and simulations of the bivariate Cuadras-Augé copula.
cBivariateCA(u1, u2, dependencyParameter, ...)
crBivariateCA(numberSimulations = 10000, seed = 42, dependencyParameter)points at which to evaluate the copula.
correlation parameter.
other parameters.
Number of simulations.
Simulation seed, 42 by default.
Function :
cBivariateCA returns the value of the copula.
crBivariateCA returns simulated values of the copula.
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.
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