Bivariate Gumbel Copula

Computes CDF, PDF and simulations of the bivariate Gumbel copula.

cBivariateGumbel(u1, u2, dependencyParameter, ...)

cdBivariateGumbel(u1, u2, dependencyParameter, ...)

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

Arguments

u1, u2

points at which to evaluate the copula.

dependencyParameter

correlation parameter.

...

other parameters.

numberSimulations

Number of simulations.

seed

Simulation seed, 42 by default.

Value

Function :

• cBivariateGumbel returns the value of the copula.

• cdBivariateGumbel returns the value of the density function associated to the copula.

• crBivariateGumbel returns simulated values of the copula.

Details

The bivariate Gumbel copula has CDF :

Examples

cBivariateGumbel(u1 = .76, u2 = 0.4, dependencyParameter = 1.4)
#> [1] 0.3554577

cdBivariateGumbel(u1 = .76, u2 = 0.4, dependencyParameter = 1.4)
#> [1] 0.9085707

crBivariateGumbel(numberSimulations = 10, seed = 42, dependencyParameter = 1.2)
#>            [,1]      [,2]
#>  [1,] 0.1282118 0.5253154
#>  [2,] 0.6636565 0.8071016
#>  [3,] 0.5948709 0.0514536
#>  [4,] 0.1923720 0.6911000
#>  [5,] 0.4399954 0.5829473
#>  [6,] 0.6241295 0.2351379
#>  [7,] 0.5411451 0.2281275
#>  [8,] 0.8487468 0.8648509
#>  [9,] 0.4072254 0.5550345
#> [10,] 0.2964031 0.4171819