LogNormalDistribution

The log-normal distribution: $\log X \sim NormalDistribution(\mu, \sigma)$ .

LogNormalDistribution(mu, sigma)an inert distribution object — carries

\mu, \sigma

, unevaluated.

Typed signatures

Type	Package	Applies
`(real, real<0..>) -> distribution`	`statistics`	always

Domain: Statistics

Details

$PDF(x) = PDF(NormalDistribution(\mu,\sigma), \log x) / x$ — delegates to compute-engine's native Normal PDF rather than writing out the Gaussian by hand.
$CDF(x) = CDF(NormalDistribution(\mu,\sigma), \log x)$ , same delegation.
$Mean = e^{\mu+\sigma^2/2}$ , $Variance = (e^{\sigma^2}-1)e^{2\mu+\sigma^2}$ , both exact.
RandomVariate draws $e^{\mu + \sigma Z}$ for a standard normal $Z$ .