bivariateCA.RdComputes CDF and simulations of the bivariate Cuadras-Augé copula.
cBivariateCA(u1, u2, dependencyParameter, ...) crBivariateCA(numberSimulations = 10000, seed = 42, dependencyParameter)
| u1, u2 | points at which to evaluate the copula. |
|---|---|
| dependencyParameter | correlation parameter. |
| ... | other parameters. |
| numberSimulations | Number of simulations. |
| seed | 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] 0.3392721crBivariateCA(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