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If X is gamma(n,$\lambda$) distributed, what should $\alpha$ and $\beta$ be such that the constructed random variable $\beta*exp(\alpha X)$ is approximated by the lognormal(0,1) distribution when n is sufficiently large. I have tried splitting the gamma variable into a sum of exponential variables and also tried Taylor expanding $\beta*exp(\alpha X)$ but neither seems to be working.

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  • $\begingroup$ What are your insights on the problem? Where exactly are you stuck? $\endgroup$ – Jan Feb 21 '17 at 0:00

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