New answers tagged independence
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Gap between the given correlation parameter and the empirical correlation in (Gaussian) copula simulation
The value of linear correlations are not preserved across nonlinear transformation of the margins. The parameter, $\rho$ measures the Pearson correlation for a Gaussian copula when the margins are ...
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4
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Series of mutually independent variables that are dependent on an auxiliary random variable
Let $\{Y_i, i=1,2,\ldots, n\}$ be any finite collection of random variables for which
(i) $\{C\} \bigcup \{Y_i\}$ are independent and
(ii) $E[|Y_i|] \lt \infty$ for all $i.$
For $i=1, 2, \ldots,$ let $...
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4
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Accepted
Series of mutually independent variables that are dependent on an auxiliary random variable
If you want an actual example then it is easier to construct the $X_i$ first and then create $C$ depending on them.
For example, you could have $X_i \sim N(0,1)$ independently and have $C=2\Phi^{-1}\...
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