Dataset funcdep_data

This dependence structure is constructed by applying the function : $$h(u_1,u_2,u_3) = (u_{1},\sin(2\pi u_{1})-\frac{u_{2}}{\pi},(1+\frac{u_{3}}{\pi^{2}})(\frac{u_{3}}{2} I_{\frac{1}{4}\ge u_1}-\sin(\pi^{x_{1}}) I_{\frac{1}{4} < u_{1}}))$$ to uniformly drawn 3-dimensional random vectors. The dataset is the ranks of \(h(u)\).

funcdep_data

Format

A matrix with 500 rows and 3 columns

The example section below gives the code to re-generate this data if needed.

Details

This dataset is studied in O. Laverny, V. Maume-Deschamps, E. Masiello and D. Rullière (2020).

References

laverny2020cort

Examples

set.seed(seed = 12,kind = "Mersenne-Twister",normal.kind = "Inversion")
x = matrix(runif(1500),500,3)
x[,2] = sin(2*pi*x[,1])-x[,2]/pi
x[,3] = (x[,3]*(x[,1]<1/4)/2 - sin(pi**(x[,1]))*(x[,1]>1/4))*(1+x[,3]/(pi^2))
funcdep_data = apply(x,2,function(x){return(rank(x,ties.method = "max"))})/(501)