Lognormal Distribution Code Example in SAS

The lognormal distribution is a continuous probability distribution. Not surprisingly, it is closely related to the Normal Distribution. A random variable $X > 0$

is Lognormally Distributed with mean $\mu$

and variance $\sigma$

if the logarithm of $X$

is normally distributed, so if $Y = \ln(X) \sim \mathcal{N}(\mu, \sigma)$

The Probability Density Function of the Lognormal Distribution is

$\begin{equation*} f(x) = \frac{1}{x \sigma \sqrt{2 \pi}} \exp \left( - \frac{(\ln(x) - \mu)^2}{2 \sigma^2} \right) \end{equation*}$

Lognormal Probability Density Function for different mean and variance

Lognormal CummulativeDensity Function for different mean and variance

I have previously written a blog post about fitting the Lognormal Distribution to univariate data in Fit Distribution to Continuous Data. Also, I use the lognormal in the post Simulate An RSLN Model in SAS.