I have a bivariate data sample $(a, b)$ which I would like to model with a joint distribution $(A, B)$. I fitted the marginal distributions for $A$ and $B$, however, the samples $a$ and $b$ are not independent. Now I transformed my data $(a, b)$ to pseudo observations to fit a suitable copula. I tested a couple of copula distributions and ranked them by their AIC values. Now my problem is, how can I visualize how well the copula distribution with the least AIC value fits my data sample?

For univariate distributions, one can plot density histograms with the chosen model, qqplots and boxplots etc., can we in some way generalize this to multivariate (or in this case just bivariate) distributions? I tried to plot coordinate-wise the qqplots and I plotted a scatterplot of a random sample of my chosen copula and the data sample, however, I feel like it does not say that much.

Most things I could find about multivariate distributions was about gaussian distributions, but neither A, B or the copula are gaussian.


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