Log-normal Distribution
Notation:
$X \sim LogNormal(\mu, \sigma)$
Probability Density Function:
$f(x)=\frac{1}{x\sqrt{2\pi \sigma^2}}
e^{-\frac{1}{2\sigma^2}(ln(x)-\mu)^2}$
where:
- $-\infty < \mu < \infty$
- $\sigma > 0$
- $x > 0$
Mean:
$\mathrm{E}[X]=e^{\mu+\sigma^2/2}$
Variance:
$\mathrm{Var}[X]=(e^{\sigma^2}-1)e^{2\mu+\sigma^2}$
Alternative Parameterizations:
References:
-
Log-normal Distribution - Wikipedia
-
Log-normal Distribution - Wolfram MathWorld