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I read a book titled "Statistics and Data Analysis for Financial Engineering with R examples". At page 203, I read the following paragraph.

"Figure 8.7 shows density histograms of both samples of uniform transformed flows as well as their scatterplot and two-dimensional KDE density contours. The histograms show some deviations from uniform distributions, which suggests that the skewed-t model may not provide adequate fits and that a semiparametric pseudo-maximum likelihood approach might be tried—this is considered below. However, the deviations may be due to random variation."

However, I do not understand why does the author assumes that the skewed-t model may not provide a best fit model just because there are some deviations from the uniform distribution. In other words, what is the relationship between skewed-t model and deviations from the uniform distribution? How can I suggest the best fit based on the histograms from the uniform distribution?

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  • $\begingroup$ I'd want to know because I thought all copulas, Gaussian or not, were built from uniform marginals $\endgroup$ – develarist Aug 26 at 16:55

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