Copula Application Among other things, I am working on dependency structures for the reliability analysis of river embankments and use Copulas for this purpose.
I have 3 questions about this:

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*Strucure

I am not yet clear when I should use the D-Vine, C-Vine or R-Vine structure? At the moment I only use the D-Vines because they are nicely structured. Do you have any literature on this or a tip on which structure is best for which application?


*Pseudo-observations

I am also trying to transform my pseudo-observations back for the Copula application in order to be able to simulate any hydrographs (incl. dependency structure). Unfortunately, that doesn't work yet either. Maybe you have a short tip here.


*Plots

I am still looking for the optimal package to plot Copula applications in a nice and simple way.
I would be very pleased to receive feedback from you.
 A: For the structure of the vine copula, there is no restriction of the type that you should use. It is completely based on you. If your data is time series, then D-vine is the best for you. If you need to connect your data with particular variable, then C-vine is the choice.
2-Transform your data back to original data requires knowing the marginal distribution of your variables, which almost unknown in real life application. You can do this in R using rvinecopulib package.
3- VineCopula is well-known R package that can help you with the computational process of vine copula model.
A: I am not sure if you are still interested. However, I will answer your questions one by one:
Structure
The general structure of the vine copula model is called R-vine. The two sub-classes
of it is called C-vine and D-vine. You can select the best for your data. The number of possible R-vine, C-vine, and D-vine are numerous. Hence, there is no way to select the best among them. However, we can select the most appropriate. By doing so, you can use the RVineStructureSelect function from the VineCopula package to do the rest for you (selecting the "best" structure, bivariate copula types, and estimating the model parameters). There is one paper that discussed the performance of all the classes of the vine copula and they conclude that the R-vine provides the best result. However, this is not the case in general but depends on your data. So, if your data is small, then you can run all these models and compare them using voung test in the VineCopula package.
Pseudo-observations
To transform your original data to copula data you can use the pobs function. To back from copula data to original data after fitting the copula model, then you can simply use qnorm for standard normal distribution margins.  For example, after fitting, say, the C-vine model, then you can just simulate it. Then, just apply the q-function to this simulated data.
Plot
All copula packages can provide you with plot functions, see for example, VineCopula, vinecopulib, vinereg, and many other packages.
