Bivariate Frank Copula

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

cBivariateFrank(u1, u2, dependencyParameter, ...)

cdBivariateFrank(u1, u2, dependencyParameter, ...)

crBivariateFrank(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 :

  • cBivariateFrank returns the value of the copula.

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

  • crBivariateFrank returns simulated values of the copula.

Details

The bivariate Frank copula has CDF :

Examples

cBivariateFrank(u1 = .76, u2 = 0.4, dependencyParameter = 0.4)
#> [1] 0.312676

cdBivariateFrank(u1 = .76, u2 = 0.4, dependencyParameter = 0.4)
#> [1] 0.9796921

crBivariateFrank(numberSimulations = 10, seed = 42, dependencyParameter = 0.2)
#>             [,1]       [,2]
#>  [1,] 0.07781765 0.51733787
#>  [2,] 0.23268617 0.50502013
#>  [3,] 0.69286870 0.05956293
#>  [4,] 0.15608423 0.72494306
#>  [5,] 0.33572568 0.51276550
#>  [6,] 0.45604514 0.05466536
#>  [7,] 0.24463017 0.01977344
#>  [8,] 0.85310143 0.87160266
#>  [9,] 0.32096890 0.50002377
#> [10,] 0.27472442 0.41526784