bivariateMO {Distributacalcul} | R Documentation |
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))
[Package Distributacalcul version 0.4.0 Index]