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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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    $\begingroup$ by $\exp(X)$ do you mean the componentwise $\exp$? $\endgroup$ – Juho Kokkala May 3 '16 at 6:49
  • $\begingroup$ Yes. I mean componentwise $\endgroup$ – user2808118 May 3 '16 at 6:49
  • $\begingroup$ 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? $\endgroup$ – barrycarter May 3 '16 at 16:05
  • $\begingroup$ Sigma is the covariance matrix $\endgroup$ – user2808118 May 3 '16 at 16:07
  • $\begingroup$ Basically, X is normally distributed with mean mu and covariance matrix Sigma $\endgroup$ – user2808118 May 3 '16 at 16:09