Let $X=\mu + \Sigma^{1/2}Z$ and $Z\sim \mathcal{N}(0,I)$. Is there a closed form for the distribution of $\exp(X)$?
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2$\begingroup$ by $\exp(X)$ do you mean the componentwise $\exp$? $\endgroup$– Juho KokkalaCommented May 3, 2016 at 6:49
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$\begingroup$ Yes. I mean componentwise $\endgroup$– user2808118Commented May 3, 2016 at 6:49
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$\begingroup$ I'm not familiar with the notation capital sigma to the 1/2. I realize you're taking a sum, but what exactly are you summing? $\endgroup$– user1566Commented May 3, 2016 at 16:05
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$\begingroup$ Sigma is the covariance matrix $\endgroup$– user2808118Commented May 3, 2016 at 16:07
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$\begingroup$ Basically, X is normally distributed with mean mu and covariance matrix Sigma $\endgroup$– user2808118Commented May 3, 2016 at 16:09
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