Log-Normal Distribution

Definition

$X\sim Log-normal(\mu ,{\sigma }^2)\iff \ln X\sim N(\mu ,{\sigma }^2)$ where $\mu \in \mathbb{R}$ is Location Parameter and $\beta \in {\mathbb{R}}^{+}$ is Scale Parameter.

Properties

PDF

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