lets suppose a bivariate empirical copula as:
for a set of data of example data we can plot it like this:
How can we compute the joint cdf of this empirical copula which should like this:
Thank you
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$\begingroup$ I know there is a function in copula package but I cant figure out how to write it myself. $\endgroup$– FredCommented Mar 6, 2015 at 21:17
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$\begingroup$ Does this help at all? Maybe I don't understand the question, but it seems like it's just a matter of curve/surface fitting. $\endgroup$– shadowtalkerCommented Mar 14, 2015 at 20:48
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$\begingroup$ The following 2 leads contain code in R of how to do the ranking step, shown in the numerator of the formula you provided, for estimating the empirical copula/joint density: - See the chosen answer to this question - Another full-on tutorial is given here $\endgroup$– develaristCommented Aug 29, 2020 at 12:34
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Your empirical CDF copula has support in [0,1]^3 (I guess your observations are n ordered triplets). So, I don´t understand your graph: what do you mean by "order" in the horizontal axis?
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1$\begingroup$ I added some more information. I am trying to compute the joint cdf of a set of 3d empirical copula (I said 2d here for simplification) and the order is just sorted data $\endgroup$– FredCommented Mar 10, 2015 at 23:29
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$\begingroup$ @Xi'an he means a 3D plot of 2 variables. In the second image, axes $x$ and $y$ are the 2 variables, while the 3rd dimension, the vertical axis $z$, is the joint probability value. So the question is about ranking paired observations from 2 variables only, not 3. $\endgroup$ Commented Aug 29, 2020 at 12:37