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In wikipedia it is stated that:

If $X \sim \operatorname{Log-\mathcal{N}}(\mu, \sigma^2)$ is distributed log-normally, then $\ln(X) \sim \mathcal{N}(\mu, \sigma^2)$ is a normal random variable.

Is the converse true?

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2 Answers 2

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Yep, if $X$ is normal, then $\exp(X)$ is log-normal.

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More on X being normal while Y=exp(X) being log-normal:

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    $\begingroup$ I would clean up all references to $Ln$ to $\ln$. $\endgroup$
    – Nick Cox
    Commented Feb 20, 2022 at 10:53

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