Is this density function well-known?

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SUMMARY

The probability density function derived from the random variable Y=e^X, where X follows a standard normal distribution (X∼N(0,1)), is f_Y(y)=\frac{e^{-\frac{1}{2} \log^2(y)}}{y\sqrt{2\pi}}. This function is recognized as the log-normal distribution, a term that reflects the property that the logarithm of a log-normally distributed variable is normally distributed. The log-normal distribution is well-documented, including a dedicated Wikipedia page that outlines its key characteristics and applications.

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mnb96
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Hello,

in a certain context I had to deal with a random variable [itex]Y=e^X[/itex], where X follows a standard normal distribution, i.e. [itex]X\sim N(0,1)[/itex].
I had to calculate the probability density function of Y, which did not seem to be difficult, and I obtained:
[tex]f_Y(y)=\frac{e^{-\frac{1}{2} \log^2(y)}}{y\sqrt{2\pi}}[/tex]

The question is: does the above density function happen to be so well-known that it already has a name?
 
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People call it the log-normal distribution. [It's a silly name: not the log of normal, but rather taking its logarithm gives you something normal. Either way, that's what it's called.]

Wikipedia has a page with the usual basic facts you'd care about: http://en.wikipedia.org/wiki/Log-normal_distribution
 
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