# Log Normal Distribution

A probability distribution $$LN(\mu, \sigma)$$ having the PDF
$p_{\mu,\sigma}(x) = \frac{\mathrm{d}}{\mathrm{d}x} \Phi_{\mu,\sigma}(\ln x) = \frac{1}{\sqrt{2\pi}\sigma x} e^{-\tfrac{(\ln x - \mu)^2}{2\sigma^2}}$
that governs the probability of products of random variables, where $$\Phi$$ is the CDF of the normal distribution.
The parameters $$\mu$$ and $$\sigma$$ are equal to the mean and standard deviation of the logarithm of $$x$$ respectively.
If $$\mu$$ is equal to zero and $$\sigma$$ is equal to one then it is known as the standard log normal distribution.

### Gallimaufry

 AKCalc ECMA Endarkenment Turning Sixteen

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