crBivariateMO returns simulated values of the copula.
Arguments
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.
Details
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.