Fréchet Upper Bound Copula

Computes CDF and simulations of the Fréchet upper bound copula.

cFrechetUpperBound(u1, u2, ...)

crFrechetUpperBound(numberSimulations = 10000, seed = 42)

Arguments

u1, u2	points at which to evaluate the copula.
...	other parameters.
numberSimulations	Number of simulations.
seed	Simulation seed, 42 by default.

Value

Function :

• cFrechetUpperBound returns the value of the copula.

• crFrechetUpperBound returns simulated values of the copula.

Details

The Fréchet upper bound copula has CDF : $$C(u_{1}, u_{2}) = \min(u_{1}, u_{2})$$ for \(u_{1}, u_{2} \in [0, 1]\).

Examples

cFrechetUpperBound(u1 = .56, u2 = 0.4)
#> [1] 0.4

crFrechetUpperBound(numberSimulations = 10, seed = 42)
#>            [,1]      [,2]
#>  [1,] 0.9148060 0.9148060
#>  [2,] 0.9370754 0.9370754
#>  [3,] 0.2861395 0.2861395
#>  [4,] 0.8304476 0.8304476
#>  [5,] 0.6417455 0.6417455
#>  [6,] 0.5190959 0.5190959
#>  [7,] 0.7365883 0.7365883
#>  [8,] 0.1346666 0.1346666
#>  [9,] 0.6569923 0.6569923
#> [10,] 0.7050648 0.7050648