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. correlation parameters, must be vector of length 2. other parameters. Number of simulations. 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