Fréchet Copula

Computes CDF and simulations of the Fréchet copula.

cFrechet(u1, u2, dependencyParameter, ...)

crFrechet(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.

Value

Function :

• cFrechet returns the value of the copula.

• crFrechet returns simulated values of the copula.

Details

The Fréchet copula has CDF : $$C(u_{1}, u_{2}) = (1 - \alpha - \beta)(u_{1} \times u_{2}) + \alpha\min(u_{1}, u_{2})% + \beta\max(u_{1} + u_{2} - 1, 0)$$ for \(u_{1}, u_{2}, \alpha, \beta \in [0, 1]\) and \(\alpha + \beta \leq 1\).

Examples

cFrechet(u1 = .76, u2 = 0.4, dependencyParameter = c(0.2, 0.3))
#> [1] 0.28

crFrechet(numberSimulations = 10, seed = 42, dependencyParameter = c(0.2, 0.3))
#>            [,1]      [,2]
#>  [1,] 0.4577418 0.4577418
#>  [2,] 0.0000000 0.0000000
#>  [3,] 0.0000000 0.0000000
#>  [4,] 0.8304476 0.1695524
#>  [5,] 0.4622928 0.4622928
#>  [6,] 0.9400145 0.9400145
#>  [7,] 0.7365883 0.2634117
#>  [8,] 0.0000000 0.0000000
#>  [9,] 0.0000000 0.0000000
#> [10,] 0.0000000 0.0000000