This dataset is a simulation of 200 points from a 3-dimensional clayton copula with \(\theta = 7\), hence highly dependent, for the first, third and fourth marginals. The second marginal is added as independent uniform draws. Lastly, the third marginal is flipped, inducing a negative dependence structure.
clayton_dataA matrix with 200 rows and 4 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
psi <- function(t,alpha) (1 + sign(alpha)*t) ^ (-1/alpha) # generator
rClayton <- function(n,dim,alpha){
val <- matrix(runif(n * dim), nrow = n)
gam <- rgamma(n, shape = 1/alpha, rate = 1)
gam <- matrix(gam, nrow = n, ncol = dim)
psi(- log(val) / gam,alpha)
}
set.seed(12,kind = "Mersenne-Twister",normal.kind = "Inversion")
clayton_data <- matrix(nrow=200,ncol=4)
clayton_data[,c(1,4,3)] = rClayton(n=200,dim=3,alpha=7)
clayton_data[,2] = runif(200)
clayton_data[,3] <- 1 - clayton_data[,3]