Fréchet Lower Bound Copula

Computes CDF and simulations of the Fréchet lower bound copula.

cFrechetLowerBound(u1, u2, ...)

crFrechetLowerBound(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 :

  • cFrechetLowerBound returns the value of the copula.

  • crFrechetLowerBound returns simulated values of the copula.

Details

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

Examples

cFrechetLowerBound(u1 = .76, u2 = 0.4)
#> [1] 0.16

crFrechetLowerBound(numberSimulations = 10, seed = 42)
#>            [,1]       [,2]
#>  [1,] 0.9148060 0.08519396
#>  [2,] 0.9370754 0.06292459
#>  [3,] 0.2861395 0.71386047
#>  [4,] 0.8304476 0.16955237
#>  [5,] 0.6417455 0.35825448
#>  [6,] 0.5190959 0.48090405
#>  [7,] 0.7365883 0.26341169
#>  [8,] 0.1346666 0.86533340
#>  [9,] 0.6569923 0.34300771
#> [10,] 0.7050648 0.29493522