bivariateMO {Distributacalcul}

Bivariate Marshall-Olkin Copula

Description

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

Usage

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

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

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.

Value

Function :

• cBivariateMO returns the value of the copula.

• crBivariateMO returns simulated values of the copula.

Examples

cBivariateMO(u1 = .76, u2 = 0.4, dependencyParameter = c(0.4, 0.3))

crBivariateMO(numberSimulations = 10, seed = 42, dependencyParameter = c(0.2, 0.5))