I'm trying to generate a bivariate random sample of the t-copula (using rho = 0.8), without using the "copula" package and its function "rCopula" with method "tCopula". I'm using the following R-code:

N <- 10000
R <- array(c(1,0.8,0.8,1), dim=c(2,2))
L <- t(chol(R)) 
Z <- rbind(rnorm(N),rnorm(N)) 
X <- L%*%Z 
df <- 2
W <- df/rchisq(N,df)
Y <- sqrt(W)*X  
plot(Y[1,],Y[2,])
U <- pt(Y,df)
plot(U[1,],U[2,])

But the plot does not look like random points from a t-copula:

![enter image description here][1] [1]: https://i.sstatic.net/3VBzw.jpg

Does anyone know if I'm making a conceptual error or a mistake in the code?

I'm trying to generate a bivariate random sample of the t-copula (using rho = 0.8), without using the "copula" package and its function "rCopula" with method "tCopula". I'm using the following R-code:

N <- 10000
R <- array(c(1,0.8,0.8,1), dim=c(2,2))
L <- t(chol(R)) 
Z <- rbind(rnorm(N),rnorm(N)) 
X <- L%*%Z 
df <- 2
W <- df/rchisq(N,df)
Y <- sqrt(W)*X  
plot(Y[1,],Y[2,])
U <- pt(Y,df)
plot(U[1,],U[2,])

But the plot does not look like random points from a t-copula:

Does anyone know if I'm making a conceptual error or a mistake in the code?

It should look more like this: (generated using the copula package and its inbuilt functions)