Gilbrat's Distribution

A Continuous Distribution in which the Logarithm of a variable $x$ has a Normal Distribution,

$$P(x)={1\over \sqrt{2\pi}} e^{-(\ln x)^2/2}.$$

It is a special case of the Log Normal Distribution

$$P(x)={1\over S\sqrt{2\pi}} e^{-(\ln x-M)^2/2S^2}.$$

with $S=1$ and $M=0$.

See also Log Normal Distribution