Lognormal Distribution

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 varianceLognormal 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.