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 if and only if 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 $\mu \in \R, \sigma \in \R_{> 0}$.

Also see

• Results about the log normal distribution can be found here.

Sources

• Weisstein, Eric W. "Log Normal Distribution." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LogNormalDistribution.html