How can I proof that the copula of an elliptical distribution $El(\mu, \sigma^2, g_n)$ is fully determined by the generator function $g_n$ and the correlation matrix extracted from $\sigma^2$.

  • $\begingroup$ Best of my knowledge, the elliptical copula does not determine by the generator function. A good book to read about Elliptical copula and how to generate it is: An introduction to copula by Nelsen 2006. $\endgroup$ – Maryam Nov 23 '18 at 8:37
  • $\begingroup$ what about: $X\backsim El(\mu,\sigma^{2},g_{n})$ -> $X-\mu\backsim El(0,\sigma^{2},g_{n})$ This is a monotonic tranformation, therefore $X-\mu$ has the same copula therefore it doesn't depend on $\mu$? $\endgroup$ – Nickpick Nov 23 '18 at 10:28
  • $\begingroup$ Could you please add the book or source for your question? Or could you please expand your question? $\endgroup$ – Maryam Nov 25 '18 at 5:12

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