Log Normal (Cobb-Douglass) Distribution

Has one shape parameter $\sigma$ >0. (Notice that the "Regress" $A=\log S$ where $S$ is the scale parameter and $A$ is the mean of the underlying normal distribution). The support is $x\ge 0$.

Notice that using JKB notation we have $\theta =L,$ $\zeta =\log S$ and we have given the so-called antilognormal form of the distribution. This is more consistent with the location, scale parameter description of general probability distributions.

Also, note that if $X$ is a log-normally distributed random-variable with $L=0$ and $S$ and shape parameter $\sigma .$ Then, $\log X$ is normally distributed with variance ${\sigma }^2$ and mean $\log S.$

Implementation: scipy.stats.lognorm