# Proof for copula determined by correlation matrix

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 $$\sigma^2$$.

• 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. – Maryam Nov 23 '18 at 8:37
• 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 $\mu$? – Nickpick Nov 23 '18 at 10:28
• Could you please add the book or source for your question? Or could you please expand your question? – Maryam Nov 25 '18 at 5:12