Computes CDF and simulations of the Fréchet copula.
cFrechet(u1, u2, dependencyParameter, ...)
crFrechet(numberSimulations = 10000, seed = 42, dependencyParameter)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.
Function :
cFrechet returns the value of the copula.
crFrechet returns simulated values of the copula.
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 \(\alpha + \beta \leq 1\).
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