Computes CDF and simulations of the bivariate Marshall-Olkin copula.

cBivariateMO(u1, u2, dependencyParameter, ...)

crBivariateMO(numberSimulations = 10000, seed = 42, dependencyParameter)

## Arguments

u1, u2 points at which to evaluate the copula. correlation parameters, must be vector of length 2. other parameters. Number of simulations. Simulation seed, 42 by default.

## Value

Function :

• cBivariateMO returns the value of the copula.

• crBivariateMO returns simulated values of the copula.

## 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.

## Examples

cBivariateMO(u1 = .76, u2 = 0.4, dependencyParameter = c(0.4, 0.3))#> [1] 0.3392721
crBivariateMO(numberSimulations = 10, seed = 42, dependencyParameter = c(0.2, 0.5))#>            [,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