Is it possible to sample a copula in the original units?

Question

I have a fairly high dimensional dataset that is not mvnormal. I used a copula to model the data and it fits well. How can I go about generating random samples from that copula that are in the original units? I.e., can I transform the uniform margins of the copula back to the original scale?

I have an example below from the palmer penguin data and the rvinecopulib.

# copula pens
library(tidyverse)
library(palmerpenguins)
library(rvinecopulib)

data("penguins")

dat <- penguins %>% na.omit() %>% filter(species=="Adelie") %>%
  select(body_mass_g,bill_depth_mm,flipper_length_mm)

# Transform the data into normalized ranks (pseudo-observations)
u <- pseudo_obs(dat) 

# Fit a vine copula model to the transformed data
fit <- vinecop(u)

# Generate 200 simulated samples from the fitted copula model
uSim <- rvinecop(n=200,fit)

Answer 1

Yes it is. Once you have a sample $u$, with uniform margins, from the copula, you need to plug each component into the the marginal distribution of your original data. The values $x_i = F(u_i)$ are then the components of your sample on the original scale.