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