Definition:Log Normal Distribution

Definition
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $\Img X = \R_{>0}$.

$X$ is said to have a log normal distribution it has probability density function:


 * $\ds \map {f_X} x = \dfrac 1 {\sigma \sqrt {2 \pi} x } \map \exp {-\dfrac {\paren {\map \ln x - \mu}^2} {2 \sigma^2} }$

for $\mu \in \R, \sigma \in \R_{> 0}$.