bivariateMO.Rd
Computes CDF and simulations of the bivariate Marshall-Olkin copula.
cBivariateMO(u1, u2, dependencyParameter, ...) crBivariateMO(numberSimulations = 10000, seed = 42, dependencyParameter)
u1, u2 | points at which to evaluate the copula. |
---|---|
dependencyParameter | correlation parameters, must be vector of length 2. |
... | other parameters. |
numberSimulations | Number of simulations. |
seed | Simulation seed, 42 by default. |
Function :
cBivariateMO
returns the value of the copula.
crBivariateMO
returns simulated values of the copula.
The bivariate Marshall-Olkin copula has CDF : $$C(u_{1}, u_{2}) = u_{1}u_{2}^{1 - \beta} \times% \textbf{1}_{\{u_{1}^{\alpha} \leq u_{2}^{\beta}\}} + % u_{1}^{1 - \alpha}u_{2} \times \textbf{1}_{\{u_{1}^{\alpha}% \geq u_{2}^{\beta}\}}$$ for \(u_{1}, u_{2}, \alpha, \beta \in [0, 1]\). It is the geometric mean of the independance and upper Fréchet bound copulas.
#> [1] 0.3392721#> [,1] [,2] #> [1,] 0.9904496 0.26361815 #> [2,] 0.9999990 0.47001156 #> [3,] 0.6165533 0.31847468 #> [4,] 0.9604149 0.13711462 #> [5,] 0.9940986 0.26671480 #> [6,] 0.9742787 0.75508067 #> [7,] 0.9065275 0.61249833 #> [8,] 0.5148039 0.06057856 #> [9,] 0.9950895 0.27542915 #> [10,] 0.9706447 0.33692591