We simulate from a density inside the piecewise linear copula class, by applying the function: $$h(u) = (u_1, \frac{u_2}{2} + \frac{1}{2}I_{u_1 \notin (\frac{1}{3}, \frac{2}{3})})$$ to a 200x2 uniform sample, and taking ranks.
impossible_dataA matrix with 200 rows and 2 columns
The example section below gives the code to re-generate this data if needed.
This dataset is studied in O. Laverny, V. Maume-Deschamps, E. Masiello and D. Rullière (2020).
laverny2020cort
set.seed(seed = 12, kind = "Mersenne-Twister", normal.kind = "Inversion")
x = matrix(runif(400),200,2)
x = t(apply(x, 1,function(u){
if(u[1]< 1/3){
u[2] = 1/2 + u[2]/2
} else{ if(u[1]<2/3){
u[2] = u[2]/2
} else {
u[2] = 1/2 + u[2]/2
}}
return(u)
}))
impossible_data = apply(x,2,function(x){return(rank(x,ties.method = "max"))})/(201)