Lognormal Distribution

Distribution Analyses

The lognormal distribution has the probability density function

$f(y) = \frac{1}{y-\theta} \frac{1}{\sqrt{2{\pi}} \sigma } \exp( - \frac{1}2 ( \frac{{\log}(y-\theta)-\zeta}{\sigma} )^2 ) {for y\gt\theta}$

where $\theta$ is the threshold parameter, $\zeta$ is the scale parameter, and $\sigma$ is the shape parameter.

The cumulative distribution function is

$F(y) = \Phi( \frac{{\log}(y-\theta)-\zeta}{\sigma} ) {for y\gt\theta}$