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I am studying copulas and I find it difficult to understand what a copula density tells me about the dependence of random variables.

For example, if I have a Gaussian copula density, what can I say about the dependence. How do I even interpret this picture?

enter image description here

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    $\begingroup$ You need to describe what this plot represents. It certainly isn't the graph of a copula! What exactly is it? $\endgroup$
    – whuber
    Commented Nov 14, 2015 at 19:25
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    $\begingroup$ @whuber This is the copula density, which we obtain after differentiation of the Gaussian copula. $\endgroup$
    – ani
    Commented Nov 14, 2015 at 19:37

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Well, the copula density is a density and can be interpreted as any other density. Specifically, with the density you have shown us, clearly the conditional distribution of one variable depends on the other, so there is dependence, not independence. Further, the density is higher (highest) for (0,0) and (1,1), and lowest for (1,0) and (0,1), so we have a positive correlation.

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    $\begingroup$ the higher density in the tails demonstrate positive correlation for extreme values. what does the higher density in the tails say about tail dependence, given that copulas allow for a separation between the concepts of correlation and tail dependence? $\endgroup$
    – develarist
    Commented Aug 30, 2020 at 14:04

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